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

We study the two dimensional dissipative quasi-geostrophic equations in the Sobolev space Existence and uniqueness of the solution local in time is proved in H^s when s>2(1–). Existence and uniqueness of the solution global in time is also proved in H^s when s2(1–) and the initial data is small. For the case, s>2(1–), we also obtain the unique large global solution in H^s provided that is small enough.Acknowledgement The author thanks Professor Jiahong Wu for useful conversations, Professor Antonio Cordoba for kindly providing their preprints and Professor Peter Constantin for kind suggestions and encouragement. This work is partially supported by the Oklahoma State University, School of Art and Science new faculty start-up fund and by the Deans Incentive Grant.