Existence and asymptotic behavior of $C^1$ solutions to the multidimensional compressible Euler equations with damping

Details Existence and asymptotic behavior of $C^1$ solutions to the multidimensional compressible Euler equations with damping Existence and asymptotic behavior of $C^1$ solutions to the multidimensional compressible Euler equations with damping

2007-03-21

arxiv.org/abs/math/0703621v1

Nonlinear Anal. TMA 70(2009) 244-261

Mathematics

Analysis of PDEs

18 pages

Scientific paper

10.1016/j.na.2007.11.049

In this paper, the existence and asymptotic behavior of $C^1$ solutions to the multidimensional compressible Euler equations with damping on the framework of Besov space are considered. We weaken the regularity requirement of the initial data, and improve the well-posedness results of Sideris-Thomases-Wang (Comm.P.D.E. 28 (2003) 953). The global existence lies on a crucial a-priori estimate which is proved by the spectral localization method. The main analytic tools are the Littlewood-Paley decomposition and Bony's para-product formula.

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