Asymptotic behavior of critical dissipative quasi-geostrophic equation in Fourier space

Abstract

In this paper we show the global existence for critical dissipative quasi-geostrophic equations if ‖θ0ˆ‖L1 is small enough; among others we prove the analyticity of such a solution. If in addition the initial condition verifies |D|−δθ0∈L1(R2) with 0<δ<1, then the solution remains regular and limt→∞⁡tδ‖θˆ(t)‖L1=0. Fourier analysis and standard techniques are used.