Abstract
This study is concerned with the large time decay estimates for weak solutions of the surface quasi-geostrophic equation with H˙−12 initial data. Due to some special observation together with applying the decay characters to the class of H˙−12-functions, we may show the upper and lower bounds of decay rates for the H˙−12 weak solution of the surface quasi-strophic equation. Moreover, as a 12-order derivative of H˙−12 weak solution, we further derive an improved upper and lower bounds of decay rates for L2 weak solution. The findings may be of independent interest and the technique can be also applied to the other related fluid dynamical model with solutions in the negative Sobolev spaces.
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