On the existence of global solutions for the 3D chemorepulsion system

Abstract

In this paper, we give sufficient conditions for global-in-time existence of classical solutions for the fully parabolic chemorepulsion system posed on a convex, bounded three-dimensional domain. Our main result establishes global-in-time existence of regular nonnegative solutions provided that $\nabla \sqrt{u}\in L^4(0,T;L^2(\Omega ))$. Our method is related to the Bakry--Émery calculation and appears to be new in this context.

14 pages; incorporated referee comments and added alternative proof

References in corpus (2)

• Global-in-time regular unique solutions with positive temperature to the 1d thermoelasticity
• Characterisations for the depletion of reactant in a one-dimensional dynamic combustion model

Cited by in corpus (1)

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