0587141 - MÚ 2025 RIV DE eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GA21-02411S
Institutional support: RVO:67985840
Keywords : compressible fluid * Navier-Stokes system * stationary solutions * stochastic forcing
OECD category: Pure mathematics
Impact factor: 1.9, year: 2022
Method of publishing: 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.
Permanent Link: https://hdl.handle.net/11104/0354416