Some remarks on a Hasegawa–Mima–Charney–Obukhov equation

This paper deals with the local Cauchy problem and the existence of weak solutions for an Hasegawa–Mima–Charney–Obukhov equation arising in geophysics and plasmas theory. This model can be obtained as an asymptotic model from the Euler equations with free surface under a quasi-geostrophic velocity field assumption. We use a parabolic regularization of the equation and a priori estimates on the solutions. Moreover, in order to pass to the limit we strongly use the Jacobian structure of the nonlinear term.