Well-posedness for the 2D dissipative quasi geostrophic equations in the Besov space

摘要

In this paper, we consider the initial value problem of the 2D dissipative quasigeostrophic equations. Existence and uniqueness of the solution global in time are proved in the homogenous Besov space Bsp,p∞with small data when1/2 ＜α≤ 1, 2/2α- 1 ＜ p ＜∞, sp = 2/p - (2α - 1).Our proof is based on a new characterization of the homogenous Besov space and Kato's method.