Boundedness criteria for a class of indirect (and direct) chemotaxis-consumption models in high dimensions

In a bounded and smooth domain omega of R-n, n > 5, we, mainly, consider for some xi, chi, delta positive and T-max is an element of (0, infinity] the zero-flux chemotaxis model with indirect signal absorption u(t) = xi?u - chi & nabla; middot (u & nabla;v), v(t) = ?v - wv, w(t) = -delta w + u, in omega x (0, T-max), equipped with sufficiently regular initial data u(x, 0) = u(0)(x) >= 0, v(x, 0) = v(0)(x) >= 0 and w(x, 0) = w(0)(x) >= 0. We establish the existence of xi* = xi*(n) > 1 such that whenever chi IIv(0)II(L)infinity((?)) obeys certain constraints, functions of n and xi (0 < xi < xi*), the initial-boundary value problem has a unique classical solution in omega x (0, infinity), which is bounded. In the frame of both direct and indirect chemotaxis models, our work (partially) improves and generalizes known results. (C) 2022 Elsevier Ltd. All rights reserved.