### On the Isothermal Compressible Euler Equations with Frictional Damping

Kun Zhao
Source: Commun. Math. Anal. Volume 9, Number 2 (2010), 77-97.

#### Abstract

This paper aims at initial-boundary value problems(IBVP) for the isothermal compressible Euler equations with damping on bounded domains. We first prove global existence and uniqueness of classical solutions for smooth initial data. Time asymptotically, it is shown that the density converges to its average over the domain and the momentum vanishes as time tends to infinity. Due to diffusion and boundary effects, the convergence rate is shown to be exponential. Second, based on the entropy principle, it is shown that similar results hold for $L^\infty$ entropy weak solutions.

First Page:
Primary Subjects: 35G25
Secondary Subjects: 35M10, 35L65
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.cma/1275586734
Zentralblatt MATH identifier: 05768072
Mathematical Reviews number (MathSciNet): MR2737756