On the long-time behavior of compressible fluid flows excited by random forcing

  • Dominic Breit

    Heriot-Watt University, Edinburgh, UK; TU Clausthal, Clausthal-Zellerfeld, Germany
  • Eduard Feireisl

    Czech Academy of Sciences, Praha, Czech Republic; TU Berlin, Germany
  • Martina Hofmanová

    Universität Bielefeld, Germany
On the long-time behavior of compressible fluid flows excited by random forcing cover
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Abstract

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 . (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.

Cite this article

Dominic Breit, Eduard Feireisl, Martina Hofmanová, On the long-time behavior of compressible fluid flows excited by random forcing. Ann. Inst. H. Poincaré Anal. Non Linéaire 41 (2024), no. 4, pp. 961–993

DOI 10.4171/AIHPC/115