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تسجيل مستخدم جديدInfluence of flux limitation on large time behavior in a three-dimensional chemotaxis-Stokes system modeling coral fertilization
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Ji Liu
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In this paper, we consider the following system $$left{begin{array}{ll} n_t+ucdot abla n&=Delta n- ablacdot(nmathcal{S}(| abla c|^2) abla c)-nm, c_t+ucdot abla c&=Delta c-c+m, m_t+ucdot abla m&=Delta m-mn, u_t&=Delta u+ abla P+(n+m) ablaPhi,qquad ablacdot u=0 end{array}right.$$ which models the process of coral fertilization, in a smoothly three-dimensional bounded domain, where $mathcal{S}$ is a given function fulfilling $$|mathcal{S}(sigma)|leq K_{mathcal{S}}(1+sigma)^{-frac{theta}{2}},qquad sigmageq 0$$ with some $K_{mathcal{S}}>0.$ Based on conditional estimates of the quantity $c$ and the gradients thereof, a relatively compressed argument as compared to that proceeding in related precedents shows that if $$theta>0,$$ then for any initial data with proper regularity an associated initial-boundary problem under no-flux/no-flux/no-flux/Dirichlet boundary conditions admits a unique classical solution which is globally bounded, and which also enjoys the stabilization features in the sense that $$|n(cdot,t)-n_{infty}|_{L^{infty}(Omega)}+|c(cdot,t)-m_{infty}|_{W^{1,infty}(Omega)} +|m(cdot,t)-m_{infty}|_{W^{1,infty}(Omega)}+|u(cdot,t)|_{L^{infty}(Omega)}rightarrow0 quadtextrm{as}~trightarrow infty$$ with $n_{infty}:=frac{1}{|Omega|}left{int_{Omega}n_0-int_{Omega}m_0right}_{+}$ and $m_{infty}:=frac{1}{|Omega|}left{int_{Omega}m_0-int_{Omega}n_0right}_{+}.$
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