List of publications

To January 2011

Book

1. J. Málek, J. Nečas, M. Rokyta, M. Růžička, Weak and measure–valued solutions to evolutionary PDE’s, Series: Applied Mathematics and Mathematical Computation 13, Chapman and Hall (CRC Press), 1996.

2. J. Málek, Z. Strakoš, Preconditioning and the Conjugate Gradient Method in the Context of Solving PDE's, Spotlight Series, SIAM, Philadelphia, 2014 (in print).

Chapter in book

1. J. Málek, K. R. Rajagopal, Mathematical properties of the equations governing the flow of fluids with pressure and shear rate dependent viscosities, Handbook of Mathematical Fluid Dynamics, Volume 4 (Eds: S. Friedlander, D. Serre) (2006), Elsevier B. V., Amsterdam, 407–444.
2. J. Málek, K. R. Rajagopal, Mathematical issues concerning the Navier-Stokes equations and some of its generalizations, Handb. Differ. Equ., Evolutionary Equations, Volume 2 (Eds: C. Dafermos, E. Feireisl) (2005), Elsevier/North Holland, Amsterdam, 371-459.

Publications in journals

Submitted

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1. M. Bulíček, P. Gwiazda, J. Málek, A. Swierczewska-Gwiazda, On Unsteady Flows of Implicitly Constituted Incompressible Fluids.

Accepted

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1. M. Bulíček, J. Málek, Y. Terasawa, On Hausdorff dimension of blow-up times relevant to weak solution of generalized Navier-Stokes fluids, Mathematical Sciences and Applications.
2. M. Bulíček, J. Frehse, J.Málek, On boundary regularity for the stress in problems of linerized elastoplasticity, International Journal of Advances in Engineering Sciences and Applied Mathematics(IJAESAM).

Published

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1. M. Bulíček, J. Málek, K. R. Rajagopal, On the need for compatibility of thermal and mechanical data in flow problems, International Journal of Engineering Science 49 (2011) 537--543.
2. M. Bulíček, R. Lewandowski, J. Málek, On evolutionary Navier-Stokes-Fourier type systems in three spatial dimensions, Comment. Math. Univ. Carolin. 52 (2011) 89-114.
3. M. Bulíček, P. Gwiazda, J. Málek, A. Swierczewska-Gwiazda, On scalar hyperbolic conservation laws with discontinuous flux, Mathematical Models and Methods in Applied Sciences 21 (2011) 89-113.
4. M. Bulíček, P. Kaplický, J. Málek, An L2-Regularity Result for the Evolutionary Stokes-Fourier system, Applicable Analysis 90 (2011) 31-45.
5. J. Hron, J. Málek, V. Průša, K. R. Rajagopal, Further remarks on simple flows of fluids with pressure dependent viscosities, Nonlinear Analysis: Real World Applications 12 (2011), 394-402.
6. M. Bulíček, L. Consiglieri, J. Málek, On solvability of a non-linear heat equation with a non-integrable convective term and data involving measures, Nonlinear Analysis: Real World Applications 12 (2011), 571-591.
7. J. Málek, K. R. Rajagopal, Compressible Generalized Newtonian Fluids, Z. Angew. Math. Phys. Z. Angew. Math. Phys. 61 (2010), 1097-1110.
8. J. Málek, V. Průša, K. R. Rajagopal, Generalizations of the Navier-Stokes fluid from a new perspective, International Journal of Engineering Science 48 (2010) 1907-1924.
9. J. Frehse, J. Málek, M. Růžička, Large data existence result for unsteady flows of inhomogeneous heatconducting incompressible fluids, Communications in Partial Differential Equations 35 (2010) 1891-1919.
10. J. Hron, J. Málek, P. Pustějovská, K. R. Rajagopal, On the Modeling of the Synovial Fluid, Advances in Tribology Volume 2010 (2010), Article ID 104957, 12 pages.
11. V. Kulvait, J. Málek, K. R. Rajagopal, Stress concentration due to an elliptic hole in a degrading linearized elastic solid, Int. J. of Applied Mechanics and Engineering 15 (2010), 35-49.
12. M. Bulíček, M. Majdoub, J. Málek, Unsteady Flows of Fluids with Pressure Dependent Viscosity in Unbounded Domains, Nonlinear Analysis: Real World Applications 11 (2010) 3968-3983.
13. M. Bulíček, J. Haslinger, J. Málek, J. Stebel, Shape optimization for Navier-Stokes equations with algebraic turbulence model: existence analysis, Appl. Math. Optim. 60 (2009), 185–212.
14. M. Bulíček, P. Gwiazda, J. Málek, A. Swierczewska-Gwiazda, On steady flows of an incompressible fluid with implicit power-law-like rheology, Advances in Calculus of Variations 2 (2009), 109–136.
15. M. Bulíček, J. Málek, K. R. Rajagopal, Mathematical analysis of unsteady flows of fluids with pressure, shear rate, and temperature dependent material moduli that slip at solid boundaries, SIAM J. Math. Anal. 41 (No.2) (2009), 665–707.
16. M. Bulíček, E. Feireisl, J. Málek, A Navier-Stokes-Fourier system for incompressible fluids with temperature dependent material coefficients, Nonlinear Anal. Real World Appl. 10 (2009), 992-1015.
17. M. Bulíček, J. Málek, and K. R. Rajagopal, Analysis of the Flows of Incompressible Fluids with pressure dependent viscosity fulfilling ν(p, •) →+∞ as p →+∞, Czechoslovak Math. J. (2009), 503-528.
18. J. Málek, Mathematical properties of flows of incompressible power-law-like fluids that are described by implicit constitutive relations, Electronic Transactions on Numerical Analysis Volume 31 (2008), 110-125.
19. J. Hron, C. Le Roux, J. Málek, K.R. Rajagopal, Flows of Incompressible Fluids subject to Naviers slip on the boundary, Comput. Math. Appl. 56 (2008), no. 8, 2128-2143.
20. E. Feireisl, J. Málek, A. Novotný, Navier’s slip and incompressible limits in domains with variable bottoms, Discrete and Continuous Dynamical Systems - Ser. S 1 (2008), 427–460.
21. J. Málek, K. R. Rajagopal, A Thermodynamics Framework for a Mixture of two Liquids, Nonlinear Anal. Real World Appl. 9 (2008) 1649–1660.
22. E. Feireisl, J. Málek, A. Novotný, I. Straškraba, Anelastic approximation as a singular limit of the compressible Navier-Stokes system, Comm. PDE’s 33 (2008), 157–176.
23. L. Diening, J. Málek, M. Steinhauer, On Lipschitz Truncations of Sobolev functions (with variable exponent) and their selected applications, ESAIM: Control, Optimization and Calculus of Variations 14 (2008) 211–232.
24. P. Gwiazda, J. Málek, A. Swierczewska, On flows of an incompressible fluid with discontinuous power-law rheology, Comput. Math. Appl. 53 (2007), no. 3-4, 531–546.
25. M. Bulíček, J. Málek, K. R. Rajagopal, Navier’s slip and evolutionary Navier-Stokes-like systems with pressure and shear-rate dependent viscosity, Indiana University Mathematics Journal 56 (No. 1) (2007), 51–86.
26. J. Málek, K. R. Rajagopal, Incompressible rate type fluids with pressure and shear-rate dependent material moduli, Nonlinear Anal. Real World Appl. 8 (No. 1) (2007), 156–164.
27. E. Feireisl, J. Málek, On the Navier-Stokes equations with temperature-dependent transport coefficients, Differ. Equ. Nonlinear Mech. (2006), 14 pp. (electronic).
28. J. Málek, D. Pražák, M. Steinhauer, On the existence and regularity of solutions for degenerate power-law fluids, Differential Integral Equations 19 (2006), 449–462.
29. J. Málek, K. R. Rajagopal, On the modeling of inhomogeneous incompressible fluid-like bodies, Mechanics of Materials 38 (2006), 233–242.
30. J. Málek, M. Růžička, V. V. Shelukhin, Herschel-Bulkley Fluids: Existence and Regularity of Steady Flows, Math. Models Methods Appl. Sci. 15 (No.12) (2005), 1845–1861.
31. J. Haslinger, J. Málek, J. Stebel, Shape optimization in problems governed by generalized Navier-Stokes equations: existence analysis, Control Cybernet. 34 (No.1) (2005), 283-303.
32. M. Bulíček, J. Málek, D. Pražák, On the dimension of the global attractor for a class of fluids with pressure dependent viscosities, Commun. Pure Appl. Anal. 4 (No.8) (2005), 805-822.
33. J. Frehse, S. Goj, J. Málek, A uniqueness result for a model for mixtures in the absence of external forces and interaction momentum, Appl. Math. 50 (2005), 527–541.
34. J. Frehse, S. Goj, J. Málek, On a Stokes-like system for mixtures of fluids, SIAM J. Math. Anal. 36 (No.6) (2005), 1259–1281.
35. M. Franta, J. Málek, K.R. Rajagopal, On steady flows of fluids with pressure and shear dependent viscosities, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2005), 651–670.
36. J. Kratochvíl, J. Málek, K.R. Rajagopal, A.S. Srinivasa, Modeling of the response of elastic plastic materials treated as a mixture of hard and soft regions, Z. Angew. Math. Phys. 55 (No.3) (2004), 500–518.
37. J. Frehse, J. Málek, M. Steinhauer, On analysis of steady flows of fluids with shear dependent viscosity based on the Lipschitz truncation method, SIAM J. Math. Anal. 34 (No.5) (2003), 1064–1083.
38. J. Hron, J. Málek, J. Nečas, K.R. Rajagopal, Numerical Simulations and Global Existence of Solutions of Two Dimensional Flows of Fluids With Pressure and Shear Dependent Viscosities, Modelling 2001 (Pilsen), Math. Comput. Simulation 61 (No.3-6) (2003), 297–315.
39. J. Málek, J. Nečas, K.R. Rajagopal, Global Analysis of the Flows of Fluids with pressure dependent viscosities, Arch. Ration. Mech. Anal. 165 (No.3) (2002), 243–269.
40. J. Málek, J. Nečas, K.R. Rajagopal, Global Existence of Solutions for Flows of Fluids with Pressure and Shear Dependent Viscosities, Appl. Math. Lett. 15 (No.8) (2002), 961–967.
41. J. Málek, D. Pražák, Large time behaviour via the method of ℓ-trajectories, J. Differential Equations 181 (2002), 243–279.
42. P. Kaplický, J. Málek and J. Stará, Global-in-time Hölder continuity of the velocity gradients for fluids with shear-dependent viscosities, NoDEA Nonlinear Differential Equations Appl. 9 (2002), 175–195.
43. J. Hron, J. Málek, K.R. Rajagopal, Simple flows of fluids with pressure dependent viscosities, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 457 (No.8) (2001), 1603–1622.
44. J. Málek, J. Nečas, M. Růžička, On weak solutions to a class of non–Newtonian incompressible fluids in bounded three-dimensional domains. The case p_2, Adv. Differential Equations 6 (2001), 257–302.
45. S. Luckhaus and J. Málek, On an evolutionary nonlinear fluid model in the limiting case, Math. Bohem. 126 (No.2) (2001), 421–428.
46. J. Hron, J.Málek and S. Turek, A numerical investigation of flows of shear-thinning fluids with applications to blood rheology, International Journal for Numerical Methods in Fluids 32 (2000), 863–879.
47. J. Málek, D. Pražák, Finite fractal dimension of the global attractor for a class of non-Newtonian fluids, Appl. Math. Lett. 13 (No.1) (2000), 105–110.
48. P. Kaplický, J. Málek, J. Stará, C1-regularity of weak solutions to a class of nonlinear fluids in two dimensions – stationary Dirichlet problem, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 259 (1999), 89–121.
49. J. Frehse, J. Málek, Boundary regularity results for models of elasto-perfect plasticity, Math. Models Methods in Appl. Sci. 9 (No.9) (1999), 1–15.
50. S. Leonardi, J. Málek, J. Nečas, M. Pokorný, On Axially Symmetric flows in R3, Z. Anal. Anwendungen 18 (No.3) (1999), 639–649.
51. J. Málek, J. Nečas, M. Pokorný and M.E. Schonbek, On possible singular solutions to the Navier–Stokes equations, Math. Nachr. 199 (1999), 97-114.
52. J. Frehse, J. Málek and M. Steinhauer, An existence result for fluids with shear dependent viscosity–steady flows, Nonlinear Anal. 30 (1997), 3041-3049.
53. J. Málek, J. Nečas, A finitedimensional Attractor for Threedimensional Flow of Incompressible Fluids, J. Differential Equations 127 (No.2) (1996), 498–518.
54. J. Málek, K.R. Rajagopal, M. Růžička, Existence and Regularity of Solutions and Stability of the Rest State for Fluids with Shear Dependent Viscosity, Math. Models Methods
55. J. Málek, M. Růžička, G. Thäter, Fractal Dimension, Attractors and Boussinesq Approximation in Three Dimensions, Acta Appl. Math. (IF=0.456) 37 (No.1-2) (1994), 83–97.
56. J. Málek, S. Turek, Non–Newtonian Flow Prediction by Divergence Free Finite Elements, Stability Appl. Anal. Contin. Media 3 (1993), 165–180.
57. J. Málek, J. Nečas, M. Růžička, On the Non–Newtonian Incompressible Fluids, Mathematical Models and Methods in Applied Sciences 3 (No.1) (1993), 35–63.
58. J. Jarušek, J. Málek, J. Nečas, V. Šverák, Variational inequality for a viscous drum vibrating in the presence of an obstacle, Rend. Mat. Appl. 12 (No. 4) (1992), 943–958.
59. J. Málek, J. Nečas, A. Novotný, Measure–valued solutions and asymptotic behavior of a multipolar model of a boundary layer, Czechoslovak Math. J. 42 (117) (1992), 549–576.
60. P. Klouček, J. Málek, Transonic flow calculation via finite elements, Apl. Mat. 33 (No.4) (1988), 296–321.

Invited publications in books

1. M. Bulíček, J. Málek, and K. R. Rajagopal, Mathematical Results Concerning Unsteady Flows of Chemically Reacting Incompressible Fluids, Partial Differential Equations and Fluid Mechanics (Eds. J. C. Robinson and J. L. Rodrigo), London Mathematical Society Lecture Note Series (No. 364) (2009), Cambridge University Press, 26–53.
2. J. Málek, Self-similar scaling in power-law fluid models, Proceedings of the Research Institute for Mathematical Sciences 1495 Mathematical Analysis in Fluid and Gas Dynamics, Conference in Honor of Tai-Ping Liu, July 11-13, 2005 (2006), 26–31.
3. J. Frehse, J. Málek, Problems due to the no-slip boundary in incompressible fluid dynamics, Geometric Analysis and Nonlinear Partial Differential Equations (eds. S. Hildebrandt, H. Karcher) , Springer, Berlin, (2003), 559–571.
4. J. Málek, D. Pražák, On the dimension of the global attractor for the modified Navier-Stokes equations , Nonlinear Problems in Mathematical Physics and Related Topics II (eds. M. Sh. Birman, S. Hildebrandt, V. A. Solonnikov, N. N. Uraltzeva), Kluwer/Plenum, New York, (2002), 267–283.
5. J. Frehse, S. Goj, J. Málek, A Stokes-like system for mixtures, Nonlinear Problems in Mathematical Physics and Related Topics II (eds. M. Sh. Birman, S. Hildebrandt, V. A. Solonnikov, N. N. Uraltzeva), Kluwer/Plenum, New York, (2002), 119–136.
6. J. Málek, Global Analysis For The Fluids Of A Power-Law Type, Differential Equations and Nonlinear Mechanics (ed. K. Vajravelu), Kluwer Academic Publishers, (2001), 213–233.
7. J. Málek, T. Roubíček, Optimization of steady flows for incompressible viscous fluids, Applied Nonlinear Analysis (eds. A. Sequeira, H. Beirao da Veiga, J.H. Videman) , Kluwer /Plenum, New York, (1999), 355–372.
8. P. Kaplický, J. Málek and J. Stará, On global existence of smooth two-dimensional steady flows for a class of non-Newtonian fluids under various boundary conditions, Applied Nonlinear Analysis (eds. A. Sequeira, H. Beirao da Veiga, J.H. Videman), Kluwer/Plenum, New York, (1999), 213–229.

Publications in proceedings

1. M. Bulíček, J. Málek, and K. R. Rajagopal, Mathematical Results Concerning Unsteady Flows of Chemically Reacting Incompressible Fluids, Partial Differential Equations and Fluid Mechanics (Eds. J. C. Robinson and J. L. Rodrigo), London Mathematical Society Lecture Note Series (No. 364) (2009), Cambridge University Press, 26-53.
2. J. Málek, Self-similar scaling in power-law fluid models, Proceedings of the Research Institute for Mathematical Sciences 1495 Mathematical Analysis in Fluid and Gas Dynamics, Conference in Honor of Tai-Ping Liu, July 11-13, 2005 (2006), 26-31.
3. J. Málek, M. Pokorný, On a certain class of singular solutions for power-law fluids, IASME Trans. 2 (No.7) (2005), 1227-1231.
4. J. Haslinger, J. Málek, J. Stebel, Shape optimization in problems governed by generalized Navier-Stokes equations: existence analysis, IASME Trans. 2 (No.7) (2005), 905-910.
5. J. Málek, G. R. Mingione, J. Stará, Fluids with pressure dependent viscosity: partial regularity of stead flows, EQUADIFF 2003, Proceedings of the international conference on differential equations (eds. F. Dumortier, H. Broer, J. Mawhin, A. Vanderbauwhede, S. Verduyn Lunel), World Sci. Publ., Singapore, (2005), 380–386.
6. J. Frehse, J. Málek, Problems due to the no-slip boundary in incompressible fluid dynamics, in: Geometric Analysis and Nonlinear Partial Differential Equations (eds. S. Hildebrandt, H. Karcher), Springer, Berlin, 2003, pp. 559-571.
7. J. Málek, D. Pražák, On the dimension of the global attractor for the modified Navier-Stokes equations, in: Nonlinear Problems in Mathematical Physics and Related Topics II (eds. M. Sh. Birman, S. Hildebrandt, V. A. Solonnikov, N. N. Uraltzeva), Kluwer/Plenum, New York, 2002, pp. 267-283.
8. J. Frehse, S. Goj, J. Málek, A Stokes-like system for mixtures, in: Nonlinear Problems in Mathematical Physics and Related Topics II (eds. M. Sh. Birman, S. Hildebrandt, V. A. Solonnikov, N. N. Uraltzeva), Kluwer/Plenum, New York, 2002, pp. 119-136.
9. J. Málek, Global Analysis For The Fluids Of A Power-Law Type, in: Differential Equations and Nonlinear Mechanics (ed. K. Vajravelu), Kluwer Academic Publishers, 2001, pp. 213-233.
10. P. Kaplický, J. Málek and J. Stará, On existence of smooth unsteady twodimensional flows for a class of non-Newtonian fluids in space periodic setting, Jubilee kateder matematiky TUL 2000 (ed. J. Vild), Technická univerzita, Liberec, (2000), 41–48.
11. J. Frehse, J. Málek, M. Steinhauer, On existence results for fluids with shear dependent viscosity – unsteady flows, Partial Differential Equations, Theory and Numerical Solution, CRC Reserach Notes in Mathematics series, Vol. 406 (eds. W. Jäger, O. John, K. Najzar, J. Nečas, J. Stará), Chapman & Hall/CRC, Boca Raton , (2000), 121–129.
12. J. Málek, T. Roubíček, Optimization of steady flows for incompressible viscous fluids, in: Applied Nonlinear Analysis (eds. A. Sequeira, H. Beirao da Veiga, J.H. Videman) , Kluwer /Plenum, New York, 1999, pp. 355-372.
13. P. Kaplický, J. Málek and J. Stará, On global existence of smooth two-dimensional steady flows for a class of non-Newtonian fluids under various boundary conditions, in: Applied Nonlinear Analysis (eds. A. Sequeira, H. Beir~ao da Veiga, J.H. Videman), Kluwer/Plenum, New York, 1999, pp. 213-229.
14. J. Málek, M. Padula, M. Růžička, A Note on Derivative Estimates for a Hopf Solution to the Navier–Stokes System in a Three–dimensional Cube, Navier–Stokes Equations and Related Non–Linear Problems (ed. A. Sequeira), Plenum, London (1995), 141–146.

Editor

1. E. Feireisl, P. Kaplický, J. Málek (Editors), Qualitative properties of solutions to partial differential equations, Lecture Notes of the Jindřich Nečas Center for Mathematical Modeling, Volume 5, Matfyzpress, 2009.
2. J. Málek, V. Průša, K.R. Rajagopal (Editors), Reviews in Geomechanics, Lecture Notes of the Jindřich Nečas Center for Mathematical Modeling, Volume 3, Matfyzpress, 2007.
3. J. Málek, J. Nečas, M. Rokyta (Editors), Advances in Mathematical Fluid Mechanics, Springer, Berlin-Heidelberg, 2000.
4. J. Málek, J. Nečas, M. Rokyta (Editors), Advanced Topics in Theoretical Fluid Mechanics, Pitman Research Notes in Mathematics Series 392, Longman Scientific and Technical, Essex, 1998.
5. P.G. Galdi, J. Málek, J. Nečas (Editors), Mathematical Theory in Fluid Mechanics, Pitman Research Notes in Mathematics Series 354, Longman Scientific and Technical, Essex, 1996.
6. P.G. Galdi, J.Málek, J. Nečas (Editors), Progress in theoretical and computational fluid mechanics, Pitman Research Notes in Mathematics Series 308, Longman Scientific and Technical, Essex, 1994.

Co-editor

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Discrete and Continuous Dynamical Systems, Series S 3 (2010), no. 3.

Discrete and Continuous Dynamical Systems, Series S 1 (2008), no. 3.

Comp. Math. Appl, 53 (2007), no. 3-4: Mechanics: The well-spring of mathematics, Volume 2

Comp. Math. Appl, 53 (2007), no. 2: Mechanics: The well-spring of mathematics, Volume 1

Appl. Mat. 51 (2006), no. 4

Appl. Mat. 49 (2004), no. 6

Appl. Mat. 47 (2002), no. 6

Thesis

1. J. Málek, Mathematical properties of the Flows of Incompressible Fluids with Pressure and Shear Rate Dependent Viscosities, DSc. thesis, Academy of Sciences of the Czech Republic, Prague (2007).
2. J. Málek, Non-newtonian incompressible fluids (mathematical theory in bounded domains), Ph.D. thesis, Faulty of Mathematics and Physics, Charles University, Prague (1992).

Others

1. E. Feireisl, J. Málek, M. Rokyta, Preface, Discrete and Conituous Dynamical Systems, Series S 1 (2008), No. 3, i-iii.
2. E. Feireisl, J. Málek, A. Novotný, M. Rokyta, M. Růžička, Foreword, Applications of Mathematics 49 (2004), 499-500.
3. I. Hlaváček, O. John, A. Kufner, J. Málek, Š. Nečasová, J. Stará, V. Šverák, Matematik Jindřich Nečas, Pokroky matematiky, fyziky a astronomie 49 (2004), 302-317.
4. I. Hlaváček, O. John, A. Kufner, J. Málek, Š. Nečasová, J. Stará, V. Šverák, In memoriam Jindřich Nečas Academy of Sciences of the Czech Republic, Mathematical Institute, Mathematica Bohemica 129 (2004), 421-446.
5. O. John, J. Málek, J. Stará, Jindřich Nečas [on the occasion of his 70th birthday], Applied Nonlinear Analysis (eds. A. Sequeira, H. Beirao da Veiga, J. H. Videman), Kluwer/Plenum, New-York, (1999), vi-xi.
6. J. Málek, T. Roubíček, J. Stará, K sedmdesátinám profesora Jindřicha Nečase (in Czech), Bulletin České společnosti pro mechaniku (1999), no. 3, 26-29.