Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space

摘要

By adapting a method in 11 with a suitable modification, we show that the critical dissipative quasi-geostrophic equations in ?~2 has global well-posedness with arbitrary H~1 initial data. A decay in time estimate for homogeneous Sobolev norms of solutions is also discussed.