### Research interests of Dalibor Pražák:

• dynamical systems, attractors and their dimension
• mathematical fluid dynamics
• nonstandard analysis

### List of publications.

#### Preprints.

• E. Feireisl, M. Petcu, D. Pražák: Relative energy approach to a diffuse interface model of a compressible two--phase flow [pdf]
• M. Bulíček, P. Kaplický, D. Pražák: Time regularity of flows of non-Newtonian fluids with critical power-law growth [pdf]

#### 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.
1. S. Frigeri, M. Grasselli, D. Pražák: Nonlocal Cahn-Hilliard-Navier-Stokes systems with shear dependent viscosity J. Math. Anal. Appl. 459 (2018), 753--777.
2. M. Michálek, D. Pražák, J. Slavík: Semilinear damped wave equation in locally uniform spaces. Commun. Pure Appl. Anal. 16 (2017), no. 5, 1673--1695.
3. D. Pražák, K. R. Rajagopal, J. Slavík: A non-standard analysis approach to a constrained forced oscillator. J. Log. Anal. 9 (2017), 1--22.
4. 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.
5. D. Pražák, K. R. Rajagopal: Mechanical oscillators with dampers defined by implicit constitutive relations. Comment. Math. Univ. Carolinae 57 (2016), no. 1, 51-61.
6. D. Pražák, J. Slavík: Nonstandard analysis of global attractors. Math. Log. Quart. 61 (2015), No. 4­5, 315--328.
7. 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.
8. 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.
9. V. Janeček, B. Andreotti, D. Pražák, T. Bárta, V. S. Nikolayev: Moving contact line of a volatile fluid. Phys. Rev. E 88, 060404 (2013).
10. 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.
11. 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.
12. D. Pražák, K. R. Rajagopal: Mechanical oscillators described by a system of differential-algebraic equations. Appl. Math. 57 (2012), issue 2, 129--142.
13. 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.
14. D. Pražák: Remarks on the uniqueness of second order ODEs. Appl. Math. 56 (2011), no. 16, 161--172.
15. 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.
16. 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.
17. 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.
18. 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.
19. 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.
20. 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.
21. 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.
22. 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.
23. 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.
24. 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.
25. D. Pražák: Exponential attractors for abstract parabolic systems with bounded delay. Bull. Austral. Math. Soc. 76 (2007), no. 2, 285--295.
26. 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.
27. D. Pražák: Exponential attractor for a planar shear-thinning flow. Math. Meth. Appl. Sci. 30 (2007), no. 17, 2197--2214.
28. D. Pražák: On the dynamics of equations with infinite delay. Cent. Eur. J. Math. 4 (2006), no. 4, 635--647.
29. 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.
30. 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.
31. 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.
32. D. Pražák: A necessary and sufficient condition for the existence of an exponential attractor. Cent. Eur. J. Math. 1 (2003), no. 3, 411--417.
33. 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.
34. J. Málek, D. Pražák: Large time behavior via the method of $\ell$-trajectories. J. Differential Equations 181 (2002), no. 2, 243--279.
35. 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.

1. 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.)
2. 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.
3. 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)
4. 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.
5. 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".)
6. D. Pražák: The Mandelbrot set. in: Proceedings of the conference Jubilanti 2000, Volume I., pp. 79--84.
7. 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.