Global bounded weak solutions to a degenerate quasilinear attraction-repulsion chemotaxis system with rotation

We consider the following quasilinear attraction-repulsion chemotaxis system with rotation {u(t) = Delta u(m) - del . (us(1)(u, v, w, x)del v) + del . (us(2)(u, v, w, x)del w), x is an element of Omega, t > 0 , v(t) = Delta v + alpha u - beta v, x is an element of Omega, t > 0, w(t) = Delta w + gamma u - delta w, x is an element of Omega, t > 0, (del u(m) - us(1) del v + us(2) del w) . v = del v . v = del w . v =0, x is an element of partial derivative Omega, t > 0, where Omega subset of R-2 is a bounded domain with smooth boundary and alpha, beta, gamma, delta are positive constants. Here S-1 = ((S) over tilde (ij))(2x2) and S-2 = ((S) over cap (ij))2x2 are chemosensitivity tensors with (S) over tilde (ij) , (S) over cap (ij) is an element of C-2 ([0, infinity)(3) x (Omega) over bar), which are assumed to satisfy vertical bar S-1 vertical bar <= C-s1 and vertical bar S-2 vertical bar <= C-s2 with some positive constants C-s1 C-s2 for all (u, v, w, x) is an element of [0, proportional to)(3) x (Omega) over bar. It is shown that whenever m > 1, for any sufficiently smooth non-negative initial data, the system possesses at least one global bounded weak solution. (C) 2016 Elsevier Ltd. All rights reserved.