Boundary Value Problems
Volume 2009 (2009), Article ID 509801, 18 pages
doi:10.1155/2009/509801

Existence and stability of steady waves for the Hasegawa-Mima equation

Abstract

By introducing a compactness lemma and considering a constrained variational problem, we obtain a set Gℝ2 of steady waves for Hasegawa-Mima equation, which describes the motion of drift waves in plasma. Moreover, we prove that Gℝ2 is a stable set for the initial value problem of the equation, in the sense that a solution ψ(t) which starts near Gℝ2 will remain near it for all time.