Global existence of solutions to a two dimensional attraction–repulsion chemotaxis system in the attractive dominant case with critical mass. (January 2020) - Nagai, Toshitaka; Yamada, Tetsuya
Abstract: We study the Cauchy problem for an attraction–repulsion chemotaxis system in two dimensions: ∂ t u = Δ u − ∇ ⋅ ( u ∇ ( β 1 v 1 − β 2 v 2 ) ), 0 = Δ v 1 − λ 1 v 1 + u, 0 = Δ v 2 − λ 2 v 2 + u with nonnegative initial data u 0 and positive constants β 1, β 2, λ 1, λ 2 . The purpose of this paper is to show that the Cauchy problem admits the global nonnegative solutions in time if ( β 1 − β 2 ) ∫ R 2 u 0 d x = 8 π in the attractive dominant case β 1 > β 2 .