Uniqueness criterion of weak solutions for the dissipative quasi-geostrophic equations in Orlicz–Morrey spaces.

Consider the quasi-geostrophic equations with the initial data. Letandbe two weak solutions with the same initial value. Ifwhereis the Orlicz–Morrey space (for a definition of this space, see Definition ), then we have. In view of the embeddingwithand, we see that our result improves the previous result of Dong and Chen. This is an extension of earlier regularity results in the Serrin’s type space. [ABSTRACT FROM AUTHOR]