Global Existence and Regularity Results for Strongly Coupled Nonregular Parabolic Systems via Iterative Methods

TL;DR

This paper establishes conditions for the global existence and regularity of solutions to strongly coupled parabolic systems using iterative methods and BMO norm estimates, extending previous results to weaker conditions.

Contribution

It introduces new weighted Gagliardo-Nirenberg inequalities involving BMO norms and shows global existence under weaker assumptions than prior work.

Findings

Global existence of classical solutions under BMO norm conditions

Introduction of new weighted Gagliardo-Nirenberg inequalities

Extension of Amann's results to weaker BMO norm conditions

Abstract

The global existence of classical solutions to strongly coupled parabolic systems is shown to be equivalent to the availability of an iterative scheme producing a sequence of solutions with uniform continuity in the BMO norms. Amann's results on global existence of classical solutions still hold under much weaker condition that their BMO norms do not blow up in finite time. The proof makes use of some new global and local weighted Gagliardo-Nirenberg inequalities involving BMO norms.