Wellposedness of Keller-Segel systems in mixed norm spaces

Abstract

We study the well-posedness of the Cauchy problem for the Keller-Segal system in the setting of mixed norm spaces. We prove existence of mild solutions n scaling invariant spaces and uniqueness in a special case. These results allow for existence and uniqueness when the initial data has anisotropic properties. In particular, persistence of anisotropic properties under the evolution is demonstrated which could be of biological interest. For more information see https://ejde.math.txstate.edu/conf-proc/26/r1/abstr.html