Global existence of weak solutions to a signal-dependent Keller-Segel model for local sensing chemotaxis

This paper is devoted to the global existence of weak solutions to the following degenerate kinetic model of chemotaxis {u(t) = Delta(gamma(v)u) (0.1) tau v(t) = Delta v - v + u in a smooth bounded domain with no-flux boundary conditions under the assumption 0 <= T < (sup gamma)((0, infinity))(-1). The problem features a positive signal-dependent (0, infinity) motility functionry gamma(.) which may vanish as v becomes unbounded. In this paper, we first modify the comparison approach developed recently in Fujie and Jiang (2020); Fujie and Jiang (2021) to derive the upper bounds of v under the slightly weakened above assumptions on gamma(.). Then by introducing a suitable approximation scheme which is compatible with the comparison method, we establish the global existence of weak solutions in any spatial dimension via compactness argument. Our weak solution has higher regularity than those obtained in previous literature (Burger et al., 2020; Desvillettes et al., 2019; Tao and Winkler, 2017). (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the global existence of weak solutions to a degenerate kinetic model of chemotaxis. By modifying the comparison method and introducing a suitable approximation scheme, the authors establish the global existence of solutions with higher regularity compared to previous literature.