Existence and asymptotic behavior of solutions to the multidimensional compressible Euler equations with damping
arXiv:math/0703621 · doi:10.1016/j.na.2007.11.049
Abstract
In this paper, the existence and asymptotic behavior of 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.
18 pages