On the uniqueness for sub-critical quasi-geostrophic equations

Abstract

Abstract. We prove uniqueness of mild solutions in the class C([0,T );L n 2γ−1 ), 0 < T ≤ ∞, for sub-critical quasi-geostrophic equations without assuming any smallness condition. As a consequence, any mild solution in C([0,∞);L 2 2γ−1 ) satisfies the regularity and decay properties given in the previous paper [4]. The proof is performed in the framework of Lorentz spaces.