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

TL;DR

This paper proves local and global existence of strong solutions for a broad class of cross diffusion systems under minimal assumptions, simplifying previous work and extending applicability.

Contribution

It establishes existence results for cross diffusion systems under VMO conditions, improving and extending prior research with more verifiable assumptions.

Findings

Proved local and global existence of strong solutions.

Reduced assumptions to VMO for solvability.

Extended previous results with more applicable conditions.

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 [16] and provides new extensions which are more verifiable in applications.