Existence and Uniqueness of the Solution to the Dissipative 2D Quasi-Geostrophic Equations in the Sobolev Space

Abstract

We study the two dimensional dissipative quasi-geostrophic equations in the Sobolev space Open image in new window Existence and uniqueness of the solution local in time is proved in H s when s>2(1−α). Existence and uniqueness of the solution global in time is also proved in H s when s≥2(1−α) and the initial data Open image in new window is small. For the case, s>2(1−α), we also obtain the unique large global solution in H s provided that Open image in new window is small enough.