Global boundedness in the higher-dimensional chemotaxis system with indirect signal production and rotational flux

We consider a chemotaxis system with indirect signal production and rotational sensitivity: {partial derivative(t)u = Delta u - del center dot (S(x, u, v, w) center dot del v) + f (u), (x, t) is an element of Omega x (0, infinity), partial derivative(t)v = Delta v - v + w, is an element of Omega x (0, infinity) partial derivative(t)w = Delta w w + u, (x, t) is an element of Omega x (0, infinity), in a smooth bounded domain Omega subset of R-N( N >= 2), where S( x, u, v, w) is an element of R-NxN is a matrix-valued function, f is a smooth function and satisfies f(0) >= 0 as well as f(s) <= kappa - mu s(alpha) for all s >= 0, where kappa >= 0, mu > 0 and alpha > 1. For all sufficiently smooth initial data, we establish the uniqueness and global boundedness of classical solution ( u, v, w) in Omega x (0,infinity) if alpha > N/4 + 1/2. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

The model considers a chemotaxis system with indirect signal production and rotational sensitivity in a smooth bounded domain, where a unique and globally bounded solution exists for sufficiently smooth initial data if certain conditions are satisfied.