Decay Estimates for Isentropic Compressible Navier-Stokes Equations in Bounded Domain

2011/04/13 by Fang, Daoyuan, Zi, Ruizhao, Zhang, Ting · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1104.2516

Abstract

In this paper, under the hypothesis that ρ is upper bounded, we construct a Lyapunov functional for the multidimensional isentropic compressible Navier-Stokes equations and show that the weak solutions decay exponentially to the equilibrium state in L² norm. This can be regarded as a generalization of Matsumura and Nishida's results in 1982, since our analysis is done in the framework of Lions 1998 and Feireisl et al. 2001, the higher regularity of (ρ, u) and the uniformly positive lower bound of ρ are not necessary in our analysis and vacuum may be admitted. Indeed, the upper bound of the density ρ plays the essential role in our proof.

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• Nonlinearity exponential stability for Lions-Feireisl's weak solutions to the three-dimensional Barotropic Compressible Navier-Stokes Equations with large Potential Force

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