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 ∇√u∈ L⁴(0, T; L²(Ω)) . Our method is related to the Bakry–Émery calculation and appears to be new in this context.
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Cieślak et al. (2024) studied this question.
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