0587141 - MÚ 2025 RIV DE eng J - Článek v odborném periodiku
Breit, D. - Feireisl, Eduard - Hofmanová, M.
On the long-time behavior of compressible fluid flows excited by random forcing.
Annales de l'Institut Henri Poincaré. Analyse non Linéaire. Roč. 41, č. 4 (2024), s. 961-993. ISSN 0294-1449. E-ISSN 1873-1430
Grant CEP: GA ČR(CZ) GA21-02411S
Institucionální podpora: RVO:67985840
Klíčová slova: compressible fluid * Navier-Stokes system * stationary solutions * stochastic forcing
Obor OECD: Pure mathematics
Impakt faktor: 1.9, rok: 2022
Způsob publikování: Open access
https://doi.org/10.4171/aihpc/115

We are concerned with the long-time behavior of the stochastic Navier-Stokes system for compressible fluids in dimensions two and three. In this setting, the part of the phase space occupied by the solution depends sensitively on the choice of the initial state. Our main results are threefold. (i) The kinetic energy of a solution is universally and asymptotically bounded, independent of the initial datum. (ii) Time shifts of a solution with initially controlled energy are asymptotically compact and generate an entire solution defined for all t 2 R. (iii) Every solution with initially controlled energy generates a stationary solution and even an ergodic stationary solution on the closure of the convex hull of its !-limit set on the space of measures on the path space.
Trvalý link: https://hdl.handle.net/11104/0354416