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• W2918183973 abstract "This paper deals with a boundary-value problem for a coupled chemotaxis-Navier-Stokes system involving tensor-valued sensitivity with saturation $$left{ begin{array}{l} n_t+ucdotnabla n=Delta n-nablacdot(nS(x,n,c)nabla c),quad xin Omega, c_t+ucdotnabla c=Delta c-c+n,quad xin Omega, t>0, u_t+kappa(u cdot nabla)u+nabla P=Delta u+nnabla phi,quad xin Omega, t>0, nablacdot u=0,quad xin Omega, end{array}right.$$ which describes chemotaxis-fluid interaction in cases when the evolution of the chemoattractant is essentially dominated by production through cells, where $kappain mathbb{R},phiin W^{2,infty}(Omega)$ and $S$ is a given function with values in $mathbb{R}^{2times2}$ which fulfills $$|S(x,n,c)| leq C_S (1 + n)^{-alpha}$$ with some $C _S > 0$ and $alpha geq 0.$ If $alpha>0$ and $Omegasubseteq mathbb{R}^2$ is a {bf bounded} domain with smooth boundary, then for all reasonably regular initial data, a corresponding initial-boundary value problem for $(KSNF)$ possesses a global classical solution which is bounded on $Omegatimes(0,infty)$. This extends a recent result by Wang-Winkler-Xiang (Annali della Scuola Normale Superiore di Pisa-Classe di Scienze. XVIII, (2018), 2036--2145) which asserts global existence of bounded solutions under the constraint $Omegasubseteq mathbb{R}^2$ is a bounded {bf convex domain} with smooth boundary. Moreover, we shall improve the result of Wang-Xiang (J. Diff. Eqns., 259(2015), 7578--7609), who proved the possibility of global and bounded, in the case that ${bfkappaequiv0}$ and $alpha>0$. In comparison to the result for the corresponding fluid-free system, the {bf optimal condition} on the parameter $alpha$ for both {bf global existence} and {bf boundedness} are obtained." @default.
• W2918183973 created "2019-03-11" @default.
• W2918183973 creator A5077280174 @default.
• W2918183973 date "2019-03-04" @default.
• W2918183973 modified "2023-09-27" @default.
• W2918183973 title "An optimal result for global classical and bounded solutions in a two-dimensional Keller-Segel-Navier-Stokes system with sensitivity" @default.
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