Global existence of solutions to the Cauchy problem of a two dimensional attraction-repulsion chemotaxis system

In this paper, we are interested in the following attraction-repulsion chemotaxis system: {u(t) - Delta u = -del . (chi u del v) + del . (xi u del w), x is an element of R-2, t > 0, v(t) + beta v - Delta v = alpha u, x is an element of R-2, t > 0, delta w - Delta w = gamma u, x is an element of R-2, t >0, u(x,0) = u(0) (x), v(x,0) = v(0)(x) x is an element of R-2, where the parameters chi, xi, alpha, beta, gamma, delta are positive and the initial data u(0), v(0) are nonnegative and u(0) not equivalent to 0. By a modified free energy functional, we establish the global existence of classical solutions when the repulsion dominates over or cancels attraction (i.e. xi gamma >= chi alpha) or the attraction dominates (i.e. xi gamma < chi alpha) and the initial cell mass parallel to u(0)parallel to(L1) ((R2)) < 8 pi/chi alpha-xi gamma. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper focuses on the attraction-repulsion chemotaxis system and establishes the global existence of classical solutions under different parameter conditions using a modified free energy functional.