Quasi-geostrophic-type equations with initial data in Morrey spaces

This paper studies the well posedness of the initial value problem for the quasi-geostrophic type equations where is a fixed parameter and is divergence free and determined from through the Riesz transform ( being a permutation of j, . The initial data is taken in certain Morrey spaces (see text for the definition). The local well posedness is proved for and the solution is global for sufficiently small data. Furthermore, the solution is shown to be smooth.

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