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Zero-electron-mass limit of hydrodynamic models for plasmas

Published online by Cambridge University Press:  04 April 2011

Jiang Xu
Affiliation:
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, People's Republic of [email protected]
Wen-An Yong
Affiliation:
Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, People's Republic of [email protected]

Abstract

This paper is concerned with the limit of the vanishing ratio of the electron mass to the ion mass in the hydrodynamic models for plasmas in critical Besov spaces. We give a new construction of approximation solutions and show that periodic initial-value problems of certain scaled hydrodynamic models have smooth solutions in a (finite) time interval where the Euler solution is known to exist. Furthermore, it is justified that, as the electron mass tends to zero, the smooth solutions converge rigorously to solutions of the incompressible Euler equations, and the definite convergence orders are also obtained.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2011

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