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Application of Orlicz regularity theory in two dimensional chemotaxis systems with logistic sources (2312.15759v1)
Published 25 Dec 2023 in math.AP
Abstract: The objective is to investigate the global existence of solutions for a degenerate chemotaxis system with logistic sources in a two-dimensional domain. It is demonstrated that the inclusion of logistic sources can exclude the occurrence of blow-up solutions, even in the presence of superlinear growth in the cross-diffusion rate. Our proof relies on the application of elliptic and parabolic regularity in Orlicz spaces and variational approach.