The well-posedness of the surface quasi-geostrophic equations in the Besov–Morrey spaces

In this paper, we develop the boundedness of Riesz transform in Morrey spaces, which generalize the corresponding result in the usual LpLp spaces. As an application of this boundedness, we establish the well-posedness and blow-up criterion for the surface quasi-geostrophic equations in the framework of Besov–Morrey spaces.