| BREZINA JAN（ぶれじな やん） | データ更新日：2023.11.28 |
准教授 ／
基幹教育院
自然科学理論系部門
| 1. | Brezina Jan, Feireisl Eduard, Novotny Antonin, On convergence to equilibria of flows of compressible viscous fluids under in/out-flux boundary conditions, Discreet and Continuous Dynamical Systems, 10.3934/dcds.2021009, 41, 8, 3615-3627, 2021.08. |
| 2. | Brezina, Jan; Macha, Vaclav, Low stratification of the complete Euler system, JOURNAL OF EVOLUTION EQUATIONS, 10.1007/s00028-020-00599-6, 21, 1, 735-761, 2021.03. |
| 3. | Brezina Jan, Kreml Ondrej, Macha Vaclav, Non-uniqueness of delta shocks and contact discontinuities in the multi-dimensional model of Chaplygin gas, NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 10.1007/s00030-021-00672-0, 28, 2, 2021.03. |
| 4. | Jan Brezina, Eduard Feireisl, Antonin Novotny, Globally bounded trajectories for the barotropic Navier–Stokes system with general boundary conditions, Communications in Partial Differential Equations, p.1-13, 2020.09. |
| 5. | Jan Brezina, Existence of measure-valued solutions to a complete Euler system for a perfect gas, RIMS Kôkyûroku, 2020.01. |
| 6. | Jan Brezina, Václav Mácha, Inviscid limit for the compressible Euler system with non-local interactions, Journal of Differential Equations, 10.1016/j.jde.2019.05.012, 2019.01, [URL], The collective behavior of animals can be modeled by a system of equations of continuum mechanics endowed with extra terms describing repulsive and attractive forces between the individuals. This system can be viewed as a generalization of the compressible Euler equations with all of its unpleasant consequences, e.g., the non-uniqueness of solutions. In this paper, we analyze the equations describing a viscous approximation of a generalized compressible Euler system and we show that its dissipative measure-valued solutions tend to a strong solution of the Euler system as viscosity tends to zero, provided the strong solution exists.. |
| 7. | Jan Brezina, Eduard Feireisl, Measure-valued solutions to the complete Euler system revisited, Zeitschrift fur Angewandte Mathematik und Physik, 10.1007/s00033-018-0951-8, 69, 3, 2018.06, [URL], We consider the complete Euler system describing the time evolution of a general inviscid compressible fluid. We introduce a new concept of measure-valued solution based on the total energy balance and entropy inequality for the physical entropy without any renormalization. This class of so-called dissipative measure-valued solutions is large enough to include the vanishing dissipation limits of the Navier–Stokes–Fourier system. Our main result states that any sequence of weak solutions to the Navier–Stokes–Fourier system with vanishing viscosity and heat conductivity coefficients generates a dissipative measure-valued solution of the Euler system under some physically grounded constitutive relations. Finally, we discuss the same asymptotic limit for the bi-velocity fluid model introduced by H.Brenner.. |
| 8. | Jan Brezina, Elisabetta Chiodaroli, Ondřej Kreml, Contact discontinuities in multi-dimensional isentropic euler equations, Electronic Journal of Differential Equations, 2018, 2018.04, In this note we partially extend the recent nonuniqueness results on admissible weak solutions to the Riemann problem for the 2D compressible isentropic Euler equations. We prove non-uniqueness of admissible weak solutions that start from the Riemann initial data allowing a contact discontinuity to emerge.. |
| 9. | Jan Brezina, Eduard Feireisl, Maximal dissipation principle for the complete Euler system, RIMS Kôkyûroku, 2018.04. |
| 10. | Jan Brezina, Eduard Feireisl, Antonin Novotny, Stability of strong solutions to the Navier–Stokes–Fourier system, SIAM Journal on Mathematical Analysis, 2018.02. |
| 11. | Jan Brezina, Eduard Feireisl, Measure-valued solutions to the complete Euler system, Journal of the Mathematical Society of Japan, 10.2969/jmsj/77337733, 70, 4, 1227-1245, 2018.01, [URL], We introduce the concept of dissipative measure-valued so- lution to the complete Euler system describing the motion of an inviscid compressible fluid. These solutions are characterized by a parameterized (Young) measure and a dissipation defect in the total energy balance. The dissipation defect dominates the concentration errors in the equations satisfied by the Young measure. A dissipative measure-valued solution can be seen as the most general concept of solution to the Euler system retaining its structural stability. In particular, we show that a dissipative measure-valued solution necessarily coincides with a classical one on its life span provided they share the same initial data.. |
| 12. | Jan Brezina, Ondřej Kreml, Václav Mácha, Dimension Reduction for the Full Navier–Stokes–Fourier system, Journal of Mathematical Fluid Mechanics, 10.1007/s00021-016-0301-6, 19, 4, 659-683, 2017.12, [URL], It is well known that the full Navier–Stokes–Fourier system does not possess a strong solution in three dimensions which causes problems in applications. However, when modeling the flow of a fluid in a thin long pipe, the influence of the cross section can be neglected and the flow is basically one-dimensional. This allows us to deal with strong solutions which are more convenient for numerical computations. The goal of this paper is to provide a rigorous justification of this approach. Namely, we prove that any suitable weak solution to the three-dimensional NSF system tends to a strong solution to the one-dimensional system as the thickness of the pipe tends to zero.. |
| 13. | Jan Brezina, Asymptotic behavior of solutions to the compressible navier-stokes equation around a time-periodic parallel flow, SIAM Journal on Mathematical Analysis, 10.1137/12089555X, 45, 6, 3514-3574, 2013.12, [URL], The global in time existence of strong solutions to the compressible Navier-Stokes equation around time-periodic parallel flows in Rn, n ≥ 2, is established under smallness conditions on Reynolds number, Mach number, and initial perturbations. Furthermore, it is proved for n = 2 that the asymptotic leading part of solutions is given by a solution of the one-dimensional viscous Burgers equation multiplied by the time-periodic function. In the case n ≥ 3 the asymptotic leading part of solutions is given by a solution of the n -1-dimensional heat equation with the convective term multiplied by the time-periodic function.. |
| 14. | Jan Brezina, Yoshiyuki Kagei, Spectral properties of the linearized compressible Navier–Stokes equation around time-periodic parallel flow , Journal of Differential Equations, http://dx.doi.org/10.1016/j.jde.2013.04.036, 255, 6, 1132-1196, 2013.09. |
| 15. | Jan Brezina, Yoshiyuki Kagei, Decay properties of solutions to the linearized compressible Navier-Stokes equation around time-periodic parallel flow, Math. Models Meth. Appl. Sci., 22, 7, 1250007 (53pages), 2012.04. |
| 16. | Jan Brezina, Asymptotic properties of solutions to the equations of incompressible fluid mechanics, Journal of Mathematical Fluid Mechanics, 10.1007/s00021-009-0301-x, 12, 4, 536-553, 2010.12, [URL], Well-accepted hypothesis in the fluid dynamics is that if the boundary of the physical domain is impermeable then the viscous fluid adheres completely to it. Many authors recently proposed mathematical justifications for this hypothesis using the so-called rugous boundary. In this Paper we want to discuss optimality of results obtained in Bucur et al. [3], Bucur and Feireisl [4] or Díaz et al. [5] and we show several corresponding examples. Finally, we extend these results for more general domains.. |
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