Research interests
of
Dalibor Pražák:
- dynamical systems, attractors and their dimension
- mathematical fluid dynamics
- nonstandard analysis
List of publications.
Preprints.
- D. Pražák, M. Zelina:
On $L^p$ semigroup to Stokes equation with dynamic boundary condition in the half-space.
arXiv:2312.04478
Book.
- E. Feireisl, D. Pražák:
Asymptotic Behavior of Dynamical Systems in Fluid Mechanics.
AIMS Series on Applied Mathematics, 4 (2010).
[book flyer]
Publications in journals.
If you are interested in any of these papers,
please send me an e-mail.
- D. Pražák, M. Zelina:
On the uniqueness of the solution and finite-dimensional attractors for the 3D flow with dynamic slip boundary condition.
Diff. Int. Equations 37 (2024), no. 11-12, 859--880.
[doi]
- D. Pražák, M. Zelina:
Strong solutions and attractor dimension for 2D NSE with dynamic boundary conditions. J. Evol. Equ. 24, 20 (2024).
[doi]
- D. Pražák, B. Priyasad:
The existence and dimension of the attractor for a 3D flow of a non-Newtonian fluid subject to dynamic boundary conditions.
Appl. Anal. 103, No. 1, 166-183 (2023).
[doi]
- D. Pražák, M. Zelina:
On linearization principle for Navier-Stokes system with dynamic slip boundary condition.
Commun. Pure Appl. Anal. 22 (2023), no. 5, 1456 -- 1476.
[doi]
- D. Pražák, V. Průša, K. Tůma:
A note on parametric resonance induced by a singular parameter
modulation.
Internat. J. Non-Linear Mech. 139 (2022), 103893.
[doi]
- L. Cherfils, E. Feireisl, M. Michálek,
A. Miranville, M. Petcu, D. Pražák:
On the compressible Navier-Stokes-Cahn-Hilliard equations with dynamic boundary conditions.
Math. Models Methods Appl. Sci. 29 (2019), No. 14, 2557--2584.
- M. Bulíček, P. Kaplický, D. Pražák:
Time regularity of flows of non-Newtonian fluids with critical power-law growth
Math. Models Methods Appl. Sci. 29 (2019), No. 6, 1207--1225.
- E. Feireisl, M. Petcu, D. Pražák:
Relative energy approach to a diffuse interface model of a compressible two--phase flow
Math Meth Appl Sci. 42 (2019), No. 5, 1465--1479.
- S. Frigeri, M. Grasselli, D. Pražák:
Nonlocal Cahn-Hilliard-Navier-Stokes systems with shear dependent viscosity
J. Math. Anal. Appl. 459 (2018), 753--777.
- M. Michálek, D. Pražák, J. Slavík:
Semilinear damped wave equation in locally uniform spaces.
Commun. Pure Appl. Anal. 16 (2017), no. 5, 1673--1695.
- D. Pražák, K. R. Rajagopal, J. Slavík:
A non-standard analysis approach to a constrained forced oscillator.
J. Log. Anal. 9 (2017), 1--22.
- D. Pražák, J. Slavík:
Attractors and entropy bounds for a nonlinear RDEs with distributed delay in unbounded domains.
Discrete Contin. Dyn. Syst. -- Series B 21 (2016), no. 4, 1259--1277.
- D. Pražák, K. R. Rajagopal:
Mechanical oscillators with dampers defined by implicit constitutive relations.
Comment. Math. Univ. Carolinae 57 (2016), no. 1, 51-61.
- D. Pražák, J. Slavík:
Nonstandard analysis of global attractors.
Math. Log. Quart. 61 (2015), No. 45, 315--328.
- T. Bárta, V. Janeček, D. Pražák:
Heat conduction problem of an evaporating liquid wedge.
Electron. J. Diff. Equ., Vol. 2015 (2015), No. 53, pp. 1-18.
- M. Grasselli, D. Pražák:
Regularity results for a Cahn-Hilliard-Navier-Stokes system
with shear dependent viscosity.
Z. Anal. Anwend. 33 (2014), no. 3, 271--288.
- V. Janeček, B. Andreotti, D. Pražák, T. Bárta, V. S. Nikolayev:
Moving contact line of a volatile fluid.
Phys. Rev. E 88, 060404 (2013).
- P. Bella, E. Feireisl, D. Pražák:
Long time behavior and stabilization to equilibria
of solutions to the Navier-Stokes-Fourier system driven by highly
oscillating unbounded external forces.
J. Dynam. Differential Equations 25 (2013), no. 2, 257--268.
- D. Pražák, J. Žabenský:
On the dimension of the attractor for a perturbed 3d
Ladyzhenskaya model.
Cent. Eur. J. Math. 11 (2013), no. 7, 1264--1282.
- D. Pražák, K. R. Rajagopal:
Mechanical oscillators described by a system of differential-algebraic equations.
Appl. Math. 57 (2012), issue 2, 129--142.
- M. Grasselli, D. Pražák:
Longtime behavior of a diffuse interface model
for binary fluid mixtures with shear dependent viscosity.
Interfaces Free Bound. 13 (2011), no. 4, 507--530.
- D. Pražák:
Remarks on the uniqueness of second order ODEs.
Appl. Math. 56 (2011), no. 16, 161--172.
- M. Bulíček, F. Ettwein, P. Kaplický, D. Pražák:
On uniqueness and time regularity of flows of power-law like non-Newtonian fluids.
Math. Meth. Appl. Sci. 33 (2010), no. 16, 1995--2010.
- M. Grasselli, D. Pražák, G. Schimperna:
Attractors for nonlinear reaction-diffusion systems
in unbounded domains via the method of short trajectories.
J. Differential Equations 249 (2010), 2287--2315.
- M. Bulíček, F. Ettwein, P. Kaplický, D. Pražák:
The dimension of the attractor for the 3D flow of a non-Newtonian fluid.
Commun. Pure Appl. Anal. 8 (2009), no. 5, 1503--1520.
- J. Jelínek, D. Pražák:
On the sign of Colombeau functions and applications
to conservation laws.
Comment. Math. Univ. Carolinae 50 (2009), no. 2, 221--243.
- M. Bulíček, D. Pražák:
A note on the dimension of the global attractor for an abstract
semilinear hyperbolic problem.
Appl. Math. Lett. 22 (2009), no. 7, 1025--1028.
- E. Feireisl, D. Pražák:
A stabilizing effect of a high-frequency driving force
on the motion of a viscous, compressible, and heat conducting fluid.
Discrete Contin. Dyn. Syst. -- Series S 2 (2009), no. 1, 95--111.
- P. Kaplický, D. Pražák:
Lyapunov exponents and the dimension of the attractor
for 2d shear-thinning incompressible flow.
Discrete Contin. Dyn. Syst. 20 (2008), no. 4, 961--974.
- M. Grasselli, D. Pražák:
Exponential attractors for a class of reaction-diffusion problems
with time delays.
J. Evol. Equ. 7 (2007), no. 4, 649--667.
- D. Pražák:
Dynamics of trajectories and the
finite-dimensional reduction of dissipative evolution equations.
Int. J. Pure Appl. Math. 40 (2007), no. 1, 65--75.
- D. Pražák:
Fourier series and the Colombeau algebra on the unit circle.
Acta Universitatis Carolinae (AUC) Math. et Phys. 48, No. 2 (2007), 81--93.
- D. Pražák:
Exponential attractors for abstract parabolic
systems with bounded delay.
Bull. Austral. Math. Soc. 76 (2007), no. 2, 285--295.
- P. Kaplický, D. Pražák:
Differentiability of the solution operator
and the dimension of the attractor for certain power-law fluids.
J. Math. Anal. Appl. 326 (2007), no. 1, 75--87.
- D. Pražák:
Exponential attractor for a planar shear-thinning flow.
Math. Meth. Appl. Sci. 30 (2007), no. 17, 2197--2214.
- D. Pražák:
On the dynamics of equations with infinite delay.
Cent. Eur. J. Math. 4 (2006), no. 4, 635--647.
- J. Málek, D. Pražák, M. Steinhauer:
On the existence and regularity
of solutions for degenerate power-law fluids.
Differential Integral Equations 19 (2006), no. 4, 449--462.
- M. Bulíček, J. Málek, D. Pražák:
On the dimension of the attractor for a class of fluids with pressure dependent viscosities.
Commun. Pure Appl. Anal. 4 (2005), no. 4, 805--822.
- D. Pražák:
On the dimension of the attractor for the wave equation with nonlinear damping.
Commun. Pure Appl. Anal. 4 (2005), no. 1, 165--174.
- D. Pražák:
A necessary and sufficient condition
for the existence of an exponential attractor.
Cent. Eur. J. Math. 1 (2003), no. 3, 411--417.
- D. Pražák:
On finite fractal dimension of the global attractor
for the wave equation with nonlinear damping.
J. Dynam. Differential Equations 14 (2002), no. 4, 763--776.
- J. Málek, D. Pražák:
Large time behavior via the method of $\ell$-trajectories.
J. Differential Equations 181 (2002), no. 2, 243--279.
- J. Málek, D. Pražák:
Finite fractal dimension of the global attractor for a
class of non-Newtonian fluids.
Appl. Math. Lett. 13 (2000), no. 1, 105--110.
Publications in proceedings.
- D. Pražák:
A remark on characterization of entropy solutions.
Computer & Mathematics with Applications (2007),
Vol. 53, Issues 3-4, pp. 453-460.
("Recent Advances in the Mathematical Analysis of
Nonlinear Phenomena", edited by K.R. Rajagopal
and J. Málek.)
- D. Pražák:
The 2d Navier-Stokes equations in the form of ODEs with
bounded delay.
WSEAS Transactions on Heat and Mass Transfer,
Vol. 1 (1), 2006, pp. 122-124.
- D. Pražák:
Exponential attractor for the delayed logistic equation
with nonlinear diffusion.
in: Dynamical Systems and Differential Equations,
ed. Wei Feng, Shouchuan Hu, Xin Lu.
Discrete and Continuous Dynamical Systems (A Supplement
Volume), 2003, pp. 717--726.
(Proceedings of 4th international
conference on Dynamical Systems and Differential Equations,
Wilmington, 2002)
- J. Málek, D. Pražák:
On the dimension of the global attractor
for the modified Navier-Stokes equations.
in "Nonlinear Problems of the Mathematical Physics and Related Topics II" (ed. M.S. Birman et al.), Kluwer Academic Publishers, 2002, pp. 267--283.
- D. Pražák:
On reducing the 2d Navier-Stokes equations
to a system of delayed ODEs.
Progress in Nonlinear Differential Equations and Their Applications,
2005, Vol. 64, pp. 403-111.
(Proceedings of "Nonlinear Elliptic and Parabolic Problems: A Special
Tribute to the Work of Herbert Amann, Zurich, 2004".)
- D. Pražák:
The Mandelbrot set.
in: Proceedings of the conference Jubilanti
2000, Volume I., pp. 79--84.
- D. Pražák:
A finite-dimensional attractor to power-law fluids.
in: Navier-Stokes Equations: Theory and Numerical Methods
(ed. R. Salvi), Pitman Research Notes in Mathematics Series 388,
pp. 237--247, Longman, Adison Wesley Longman, Essex, 1998.