This paper is concerned with the fractional quasigeostrophic equation with modified dissipativity. We prove the local existence of solutions in Sobolev spaces for the general initial data and the global existence for the small initial data when .
Yongqiang Xu. "Well-Posedness of the Two-Dimensional Fractional Quasigeostrophic Equation." J. Appl. Math. 2013 1 - 6, 2013. https://doi.org/10.1155/2013/348513