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- W4380538403 abstract "The following chemotaxis-fluid system $ begin{equation*} left{ begin{split} &n_t = Delta n-chinablacdotleft(nnabla{c}right)+nc, &;;xin Omega, t>0, & c_t = Delta c-{bf u}cdotnabla c-nc, &;;xin Omega, t>0, &{bf u}_t+kappa({bf u}cdotnabla){bf u}+nabla{P} = Delta{ {bf u}}+nnablaphi , & ;;xin Omega, , t>0, &nablacdot {bf u} = 0, &;; xin Omega, , t>0 end{split} right. end{equation*} $ is considered under homogeneous Neumann boundary conditions in a bounded convex domain $ Omegasubset mathbb{R}^d (din {2, 3}) $ with smooth boundary. For $ d = 2 $, it is shown that the corresponding chemotaxis-Navier-Stokes system possesses a globally bounded classical solution which stabilizes toward a spatially homogeneous equilibrium in the sense that$ begin{equation*} begin{split} n(cdot, t)rightarrow n_infty, quad c(cdot, t)rightarrow 0 text{ and } {bf u}(cdot, t)rightarrow {bf 0} text{ in } L^infty(Omega) end{split} end{equation*} $as $ trightarrow infty $, where $ n_infty $ is a constant satisfying $ n_inftygeqfrac{1}{|Omega|}int_{Omega}n_0 $. For $ d = 3 $, it is seen that the corresponding chemotaxis-Stokes system possesses a globally defined weak solution." @default.
- W4380538403 created "2023-06-14" @default.
- W4380538403 creator A5076497458 @default.
- W4380538403 date "2023-01-01" @default.
- W4380538403 modified "2023-09-29" @default.
- W4380538403 title "Global solvability and stabilization in a chemotaxis(-Navier)-Stokes system with proliferation" @default.
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- W4380538403 doi "https://doi.org/10.3934/dcdsb.2023104" @default.
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