Local and Global Existence of Strong Solutions to Large Cross Diffusion Systems

Abstract

We study the solvability of a general class of cross diffusion systems and establish the local and global existence of their strong solutions under the weakest assumption that they are VMO. This work simplifies the setting in our previous work [15] and provides new extensions which are more verifiable in applications.

Keywords

• cross diffusion systems
• hölder regularity
• global existence
• 35j70
• 35b65
• 42b37