Boundary Value Problems
Volume 2007 (2007), Article ID 56945, 10 pages
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

Academic Editor: Patrick J. Rabier

Copyright © 2007 Jiang Xu and Daoyuan Fang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.