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  • Research Article
  • Open Access

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

Boundary Value Problems20072007:056945

  • Received: 3 July 2007
  • Accepted: 30 August 2007
  • Published:


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.


  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Equation
  • Sobolev Space


Authors’ Affiliations

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China
Department of Mathematics, Zhejiang University, Hangzhou, 310027, China


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© J. Xu and D. Fang 2007

This article is published under license to BioMed Central Ltd. 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.