Existence and uniqueness of global solution of the Hasegawa–Mima equation

Abstract

The Hasegawa–Mima equation is the simplest nonlinear model to investigate drift waves and drift-wave turbulence. In this article, we establish the existence and uniqueness of a global weak solution for the Cauchy problem of the two-dimensional Hasegawa–Mima equation. Moreover, if the background particle density is homogeneous in the x-direction, there is a unique global regular solution.