Global well-posedness for a modified dissipative surface quasi-geostrophic equation in the critical Sobolev space H1

In this paper, we consider the following modified quasi-geostrophic equations where α ]0,1[ is a fixed parameter. This equation was recently introduced by P. Constantin, G. Iyer and J. Wu (2001) in [4] as a modification of the classical quasi-geostrophic equation. In this paper, we prove that for any initial data θ in the Sobolev space , Eq. (MQG) has a global and smooth solution θ in .