Boundary Value Problems 
Volume 2007 (2007), Article ID 56945, 10 pages
doi:10.1155/2007/56945
Research Article

A Note on the Relaxation-Time Limit of the Isothermal Euler Equations

Jiang Xu1 and Daoyuan Fang2

 1Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2Department of Mathematics, Zhejiang University, Hangzhou 310027, China
Received 3 July 2007; Accepted 30 August 2007

Recommended by Patrick J. Rabier

Abstract

This work is concerned with the relaxation-time limit of the multidimensional isothermal Euler equations with relaxation. We show that Coulombel-Goudon's results (2007) can hold in the weaker and more general Sobolev space of fractional order. The method of proof used is the Littlewood-Paley decomposition.