Convergence to equilibrium for the solution of the full compressible Navier-Stokes equations

Zhang, Zhifei; Zi, Ruizhao

Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 2, pp. 457-488.

We study the convergence to equilibrium for the full compressible Navier-Stokes equations on the torus ${\mathbb{T}}^3$. Under the conditions that both the density ρ and the temperature θ possess uniform in time positive lower and upper bounds, it is shown that global regular solutions converge to equilibrium with exponential rate. We improve the previous result obtained by Villani in (2009) [28] on two levels: weaker conditions on solutions and faster decay rates.

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