Local and global strong solutions for SQG in bounded domains

We prove local well-posedness for the inviscid surface quasigeostrophic (SQG) equation in bounded domains of R2. When fractional Dirichlet Laplacian dissipation is added, global existence of strong solutions is obtained for small data for critical and supercritical cases. Global existence of strong solutions with arbitrary data is obtained in the subcritical cases.