Global classical solvability and stabilization in a two-dimensional chemotaxis-Navier-Stokes system involving Dirichlet boundary conditions for the signal

The chemotaxis-Navier-Stokes system {n(t) + u . del n = Delta n - del . (n chi(n)del c), c(t) + u . del c = Delta c - nc, u(t) + (u . del) u = Delta u + del P + n del phi, del . u = 0 is considered in a smoothly bounded domain Omega subset of R-2 under the boundary conditions (del n - n chi(n)del c) . nu = 0, c = c(star), u = 0, x is an element of partial derivative Omega, t > 0 with a given nonnegative constant c(star). It is shown that if chi is an element of C-2([0, infinity)) and chi(n) -> 0 as n -> infinity, then for all suitably regular initial data, an associated initial value problem possesses a globally defined and bounded classical solution. When parallel to n(0)parallel to(L1(Omega)) and parallel to c(0)parallel to(L infinity(Omega)) are suitably small and c(star) equivalent to 0, we further obtain the stabilization of the classical solution. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.