Boundary Value Problems
Volume 2007 (2007), Article ID 56945, 10 pages
A Note on the Relaxation-Time Limit of the Isothermal Euler Equations
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.