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Open Access Research Article

Existence and Stability of Steady Waves for the Hasegawa-Mima Equation

Boling Guo1 and Daiwen Huang12*

Author Affiliations

1 Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

2 Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

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Boundary Value Problems 2009, 2009:509801  doi:10.1155/2009/509801

Published: 5 March 2009

Abstract

By introducing a compactness lemma and considering a constrained variational problem, we obtain a set of steady waves for Hasegawa-Mima equation, which describes the motion of drift waves in plasma. Moreover, we prove that is a stable set for the initial value problem of the equation, in the sense that a solution which starts near will remain near it for all time.