Published Papers

[1] Pokorný, M.: Cauchy problem for the non-Newtonian viscous incompressible fluid, Appl. Math. 41 (1996), no. 3, 169—201.

[2] Pokorný, M.: Steady plane flow of second-grade fluid in exterior domains, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 36 (1997), 167—177.

[3] Málek, J.; Nečas, J.; Pokorný, M.; Schonbek, M. E.: On possible singular solutions to the Navier-Stokes equations, Math. Nachr. 199 (1999), 97—114.

[4] Leonardi, S.; Málek, J.; Nečas, J.; Pokorný, M.: On axially symmetric flows in R3, Z. Anal. Anwendungen 18 (1999), no. 3, 639—649.

[5] Kračmar, S.; Novotný, A.; Pokorný, M.: Estimates of three-dimensional Oseen kernels in weighted Lp spaces, In: Applied nonlinear analysis, 281-316, Kluwer/Plenum, New York, 1999.

[6] Pokorný, M.: Steady flow of viscoelastic fluid past an obstacle-asymptotic behaviour of solutions, In: Partial differential equations (Praha, 1998), 283-289, Chapman & Hall/CRC Res. Notes Math., 406, Chapman & Hall/CRC, Boca Raton, FL, 2000.

[7] Novotný, A.; Pokorný, M.: Three-dimensional steady flow of viscoelastic fluid past an obstacle, J. Math. Fluid Mech. 2 (2000), no. 3, 294-314.

[8] Farwig, R.; Novotný, A.; Pokorný, M.: The fundamental solution of a modified Oseen problem, Z. Anal. Anwendungen 19 (2000), no. 3, 713-728.

[9] Neustupa, J.; Pokorný, M.: An interior regularity criterion for an axially symmetric suitable weak solution to the Navier-Stokes equations, J. Math. Fluid Mech. 2 (2000), no. 4, 381-399.

[10] Kračmar, S.; Novotný, A.; Pokorný, M.: Estimates of Oseen kernels in weighted Lp spaces, Journal of Math. Soc. Japan 53 (2001), no. 1, 59-111.

[11] Pokorný, M.; Trojek, P.: Some notes to certain modifications of the Oseen problem, Acta Univ. Palack. Olomuc., Fac. Rerum Natur. Math. 39 (2000), 169-182.

[12] Neustupa, J.; Pokorný, M.: Axisymmetric flow of Navier-Stokes fluid in the whole space with non-zero angular velocity component, Mathematica Bohemica, 126 (2001), no. 2, 469-481.

[13] Padula, M.; Pokorný M.: Stability and decay to zero of the L2 norms of perturbations to a viscous compressible heat conductive fluid motion exterior to a ball, J. Math. Fluid Mech., 3 (2001), no. 4, 342-357.

[14] Montgomery-Smith, S.; Pokorný M.: A counterexample to the smoothness of the solution to an equation arising in fluid mechanics,Comment. Math. Univ. Carolinae, 43 (2002), no. 1, 61-75.

[15] Novo, S.; Novotný, A.; Pokorný M.: Some notes to the transport equation and to the Green formula, Rend. Sem. Math. Univ. Pad. 106 (2001) 65-76.

[16] Novotný, A.; Pokorný M.: Steady plane flow of viscoelastic fluid past an obstacle, Applications of Math. 47 (2002) 231-254.

[17] Galdi, G.P., Vaidya, A., Pokorný M., Joseph, D.D., Feng, J.: Orientation of symmetric bodies falling in a second-order liquid at nonzero Reynolds number, Mathematical Models & Methods in Applied Sciences 12 (2002) 1653-1690.

[18] Pokorný M.: A regularity criterion for the angular velocity component in the case of axisymmetric Navier-Stokes equations, Proceedings of the 4th European Congress on Elliptic and Parabolic Problems, Rolduc and Gaeta 2001, World Scientific, 2002, 233-242.

[19] Pokorný M.: On the result of He concerning the smoothness of solutions to the Navier-Stokes equations, Electronic Journal of Differential Equations 2003/11, 1-8.

[20] Penel, P.; Pokorný M.: Some new regularity criteria for the Navier--Stokes equations containing gradient of the velocity, Applications of Mathematics 49 (2004), 483-493.

[21] Novo, S.; Novotný A.; Pokorný M.: Steady compressible Navier--Stokes equations in domains with non-compact boundaries, Math. Methods Appl. Sci. 28 (2005), 1445--1479.

[22] Málek, J.; Pokorný M.: On a certain class of singular solutions for power-law fluids, IASME Transactions 7, Vol. 2 (2005), 1227--1231.

[23] Pokorný M.: A short note on regularity criteria for the Navier--Stokes equations containing the velocity gradient, Banach Center Publications, Vol. 70: Regularity and other aspects of the Navier-Stokes Equations (2005), 199--207.

[24] Mucha P.B.; Pokorný M.: On a new approach to the issue of existence and regularity for the steady compressible NavierStokes equations, Nonlinearity, 19  (2006), No. 8, 1747--1768.

[25] Kreml O.; Pokorný M.: A regularity criterion for the angular velocity component in axisymmetric Navier-Stokes equations, Electronic Journal of Differential Equations 2007, No. 08, 1--10.

[26] Novotný A.; Pokorný M.: Stabilization to equilibria of compressible Navier-Stokes equations with infinite mass, Comp. Math. Appl. 53 (2007), No. 3--4, 437--451.

[27] Pokorný M.; Mucha P.B.: 3D steady compressible Navier-Stokes equations, Discrete Contin. Dyn. Syst. Ser. S 1 (2008), No. 1, 151--163.

[28] Mucha P.B.; Pokorný M.: On the Steady Compressible Navier--Stokes--Fourier System, Communications in Mathematical Physics 288 (2009) No. 1, 349--377.

[29] Kreml, O.; Pokorný M.: On the local strong solutions for a system describing the flow of a viscoelastic fluid, Banach Center Publications, Vol. 86: Nonlocal and Abstract Parabolic Equations and their Applications (2009), 196--205.

[30] Zhou, Y.; Pokorný, M.: On a regularity criterion for the Navier-Stokes equations involving gradient of one velocity component, Journal of Mathematical Physics 50 (2009), 123514, 11p.

[31] Kreml, O.; Pokorný M.: On the local strong solutions for the FENE dumbbell model, Discrete and Continuous Dynamical Systems, Series3 (2010), No. 2, 311—324.

[32] Zhou, Y.; Pokorný, M.: On the regularity of the solutions of the Navier-Stokes equations via one velocity component, Nonlinearity 23 (2010), 1097--1107.

[33] Mucha, P.B.; Pokorný, M.: Weak solutions to equations of steady compressible heat conducting fluids, Mathematical Models and Methods in Applied Sciences 20 (2010) No. 5, 785—813.

[34] Pecharová, P.; Pokorný, M.: Steady compressible Navier-Stokes-Fourier system in two space dimensions, Comment. Math. Univ. Carolin. 51 (2010), No. 4, 653—679.

[35] Novotný, A.; Pokorný, M.: Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions, Appl. Math. 56 (2011), No. 1, 137—160.

[36] Novotný, A.; Pokorný, M.: Weak solutions for steady compressible Navier-Stokes-Fourier system for monoatomic gas and its generalizations, J. Differential Equations 251 (2011),  No. 2, 270—315.

[37] Novotný, A.; Pokorný, M.: Weak and variational solutions to steady equations for compressible heat conducting fluids, SIAM J. --Math. Anal. 43 (2011), No. 3, 1158—1188.

[38] Penel, P.; Pokorný, M.: On anisotropic regularity criteria for the solutions to 3D Navier-Stokes Equations, J. Math. Fluid Mech. 13 (2011), No. 3, 341—353.

[39] Pokorný, M.: On the steady solutions to a model of compressible heat conducting fluid in two space dimensions, J. Part. Diff. Eq. 24 (2011), No. 4, 334—350.

[40] Kubica, A., Pokorný, M., Zajšckowski, W.: Remarks on regularity criteria for axially symmetric weak solutions to the Navier-Stokes equations, Math. Methods Appl. Sci. 35 (2012), No. 3, 360—371. DOI: 10.1002/mma.1586.
 
[41] Naumann, J., Pokorný, M., Wolf, J.: On the existence of weak solutions to the equations of steady flow of heat-conducting fluids with dissipative heating, Nonlinear Analysis, Series B: Real World Applications 13 (2012), No. 4, 1600—1620. DOI:10.1016/j.nonrwa.2011.11.018.
 
[42] Feireisl, E., Mucha, P.B., Novotný, A., Pokorný, M.: Time-periodic solutions to the full Navier-Stokes-Fourier system, Arch. Ration. Mech. Anal. 204 (2012), No. 3, 745—786. DOI:10.1007/s00205-012-0492-9.
 
[43] Penel, P., Pokorný, M.: Improvement of some anisotropic regularity criteria for the NavierStokes equations, Discrete and Continuous Dynamical Systems, Series6 (2013), No. 5, 1401—1407. DOI:10.3934/dcdss.2013.6.1401.
 
[44] Kreml, O., Nečasová, Š., Pokorný, M.: On the steady equations for compressible radiative gas, Zeitschrift für angewandte Mathematik und Physik  64 (2013), 539—571. DOI: 10.1007/s00033-012-0246-4.
 
[45] Mucha, P.B., Pokorný, M., Zatorska, E.: Chemically reacting mixtures in terms of degenerated parabolic setting, Journal of Mathematical Physics, 54 (2013), 071501. DOI: 10.1063/1.4811564.
 
[46] Pokorný, M: Navier-Stokesovy rovnice: slabé řešení, jeho jednoznačnost a regularita, Kvaternion 2/2013, 83—101.
 
[47] Jesslé, D., Novotný, A., Pokorný, M.: Steady NavierStokes—Fourier  system with slip boundary conditions, Math. Models Methods Appl. Sci.  24 
(2014), No. 4, 751–781.
DOI: 10.1142/S0218202513500668.
 
[48] Mucha, P.B., Pokorný, M., Zatorska, E.: Approximate solutions to a model of two-component reactive flow, Discrete and Continuous Dynamical Systems, Series7 (2014), No. 5, 1079—1099. DOI: 10.3934/dcdss.2014.7.1079. 

[49] Mucha, P.B., Pokorný, M.:  The Rot-Div System in Exterior Domains, J. Math. Fluid Mech. 16 (2014), No. 4, 701—720. DOI: 10.1007/s00021-014-0181-6.

[50] Piasecki, T., Pokorný, M.:  Strong solutions to the NavierStokes–Fourier system with slip–inflow boundary conditions, Zeitschrift für angewandte Mathematik und Mechanik 94 (2014), No. 12, 1035—1057. DOI: 10.1002/zamm.201300014.

[51] Axmann, Š., Pokorný, M.: Time-periodic solutions to the full NavierStokes–Fourier system with radiation on the boundary, Journal of mathematical Analysis and Applications 428 (2015), 414—444. DOI: 10.1016/j.jmaa.2015.03.023.

[52] Kreml, O., Pokorný, M., Šalom, P.: On the global existence for a regularized model of viscoelastic non-Newtonian fluid, Colloquium Mathematicum 139 (2015), No. 2, 149—163. DOI: 10.4064/cm139-2-1.

[53] Farwig, R., Pokorný, M.:  A Linearized Model for Compressible Flow past a Rotating Obstacle: Analysis via Modified Bochner-Riesz Multipliers, Z. Anal. Anwend. 34 (2015), No. 3, 285—308. DOI: 10.4171/ZAA/1540.

[54] Mucha, P. B.; Pokorný, M.; Zatorska, E.: Heat-Conducting, Compressible Mixtures with Multicomponent Diffusion: Construction of a Weak Solution. SIAM J. Math. Anal. 47 (2015), No. 5, 3747—3797. DOI: 10.1137/140957640.

[55] Giovangigli, V.; Pokorný, M.; Zatorska, E.: On the steady flow  of reactive gaseous mixture.  Analysis 35  (2015), No. 4, 319-341. DOI: 10.1515/anly-2014-1306. 

Papers accepted for publication

[1] Axmann, Š., Pokorný, M.:  A generalization of some regularity criteria to the Navier-Stokes
equations involving one velocity component, to appear in Recent Developments of Mathematical Fluid Mechanics,Series: Advances in Mathematical Fluid Mechanics, Birhäuser-Verlag, Edited by Giovanni P. Galdi, John G. Heywood and Rolf Rannacher



Thesis


[1] Pokorný M.: Cauchy problem for the non-newtonian, viscous, incompressible fluid, Master degree thesis (1993).

[2] Pokorný, M.: Asymptotic behaviour of solutions to certain PDE's describing the flow of fluids, Ph.D. thesis (1999).

[3] Pokorný, M.: Matematická analýza parciálních diferenciálních rovnic popisujících proudění newtonovských tekutin, Habilitation thesis (in Czech) (2007).

 

Other publications

[1] Nečasová, Š.; Petzeltová, H.; Pokorný, M.; Sequeira, A.: To the 70th anniversary of birthday of Prof. Nečas, Mathematica Bohemica, 126 (2001), no. 2, 257-263.

 

Editorial work

[1] Nečasová, Š.; Petzeltová, H.; Pokorný, M.; Sequeira, A.: Proceedings of Partial Differential Equations and Applications, Olomouc 1999, special volume of Mathematica Bohemica, 126 (2001).

[2] Dafermos, C.; Pokorný, M.: Handbook of Differential Equations. Evolutionary Equations, Volume 4, Elsevier, 2008.

[3] Dafermos, C.; Pokorný, M.: Handbook of Differential Equations. Evolutionary Equations, Volume 5, Elsevier, 2009.

[4]  Nečasová, Š.; Šverák, V.; Pokorný, M.: Selected Works of Jindřich Nečas (PDEs, Continuum Mechanics and Regularity), Birkhauser, 2015.