Relaxation Limit in Besov Spaces for Compressible Euler Equations

2011/09/18 by Jiang Xu, Xu, Jiang, Zejun Wang +1 · 3 citations
Mathematics · #Navier-Stokes equation solutions #Gas Dynamics and Kinetic Theory #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1109.3835

Abstract

The relaxation limit in critical Besov spaces for the multidimensional compressible Euler equations is considered. As the first step of this justification, the uniform (global) classical solutions to the Cauchy problem with initial data close to an equilibrium state are constructed in the Chemin-Lerner's spaces with critical regularity. Furthermore, it is shown that the density converges towards the solution to the porous medium equation, as the relaxation time tends to zero. Several important estimates are achieved, including a crucial estimate of commutator.

Citations

• The Cauchy problem for quasi-linear symmetric hyperbolic systems

Cited by

• Relaxation limit and asymptotic stability for the Euler-Navier-Stokes equations
• Compressible Euler equations with time-dependent damping in the critical regularity setting: global well-posedness and strong relaxation limit
• Zero-relaxation and vanishing-damping limits of pressureless Euler system

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