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 quasi-geostrophic equations. Existence and uniqueness of the solution global in time are proved in the homogenous Besov space B_(p,∞)~(s_p) small data when 1/2 < α ≤ 1, 2/(2α - 1) < p < ∞, s_p = 2/p - (2α - 1). Our proof is based on a new characterization of the homogenous Besov space and Kato's method.