Open Access

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

Boundary Value Problems20092009:509801

DOI: 10.1155/2009/509801

Received: 28 September 2008

Accepted: 18 February 2009

Published: 5 March 2009

Abstract

By introducing a compactness lemma and considering a constrained variational problem, we obtain a set https://static-content.springer.com/image/art%3A10.1155%2F2009%2F509801/MediaObjects/13661_2008_Article_851_IEq1_HTML.gif of steady waves for Hasegawa-Mima equation, which describes the motion of drift waves in plasma. Moreover, we prove that https://static-content.springer.com/image/art%3A10.1155%2F2009%2F509801/MediaObjects/13661_2008_Article_851_IEq2_HTML.gif is a stable set for the initial value problem of the equation, in the sense that a solution https://static-content.springer.com/image/art%3A10.1155%2F2009%2F509801/MediaObjects/13661_2008_Article_851_IEq3_HTML.gif which starts near https://static-content.springer.com/image/art%3A10.1155%2F2009%2F509801/MediaObjects/13661_2008_Article_851_IEq4_HTML.gif will remain near it for all time.

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Authors’ Affiliations

(1)
Institute of Applied Physics and Computational Mathematics
(2)
Department of Mathematical Sciences, Tsinghua University

Copyright

© B. Guo and D. Huang. 2009

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.