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- W3021536385 abstract "This paper is concerned with the effects of nonlinear diffusion on global solvability and stabilization in a variety of models which generalizes the following prototype{nt+u⋅∇n=∇⋅(nm−1∇n)−∇⋅(n∇c)−ρn,ct+u⋅∇c=Δc−c+ρ,ρt+u⋅∇ρ=Δρ−ρn,ut+∇P=Δu+(n+ρ)∇ϕ,∇⋅u=0 with a given function ϕ∈W2,∞(Ω), where Ω⊂R3 is a general bounded domain with smooth boundary. Based on an energy-type argument combined with maximal Sobolev regularity theory, we conclude that ifm>3733, an associated initial-boundary value problem admits at least one globally bounded weak solution which stabilizes toward the spatial homogeneous equilibrium (n∞,ρ∞,ρ∞,0) in the sense that‖n(⋅,t)−n∞‖Lp(Ω)+‖c(⋅,t)−ρ∞‖W1,∞(Ω)+‖ρ(⋅,t)−ρ∞‖W1,∞(Ω)+‖u(⋅,t)‖L∞(Ω)→0ast→∞ for any p>1, where n∞:=1|Ω|{∫Ωn0−∫Ωρ0}+ and ρ∞:=1|Ω|{∫Ωρ0−∫Ωn0}+." @default.
- W3021536385 created "2020-05-13" @default.
- W3021536385 creator A5049225160 @default.
- W3021536385 date "2020-10-01" @default.
- W3021536385 modified "2023-09-25" @default.
- W3021536385 title "Large time behavior in a three-dimensional degenerate chemotaxis-Stokes system modeling coral fertilization" @default.
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- W3021536385 doi "https://doi.org/10.1016/j.jde.2020.04.039" @default.
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