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- W2922367908 abstract "This paper investigates the following Keller-Segel-Navier-Stokes system with nonlinear diffusion and rotational flux $$begin{align}begin{cases} &n_t+ucdotnabla n=Delta n^m-nablacdot(nS(x, n, c)nabla c),quad &xin Omega, t>0, &c_t+ucdotnabla c=Delta c-c+n,quad &xin Omega, t>0, &u_t+kappa (ucdotnabla)u+nabla P=Delta u+nnabla phi,quad &xin Omega, t>0, &nablacdot u=0,quad &xin Omega, t>0, end{cases}end{align}$$ where $kappain mathbb{R},phiin W^{2,infty}(Omega)$ and $S$ is a given function with values in $mathbb{R}^{2times2}$ which fulfills $$ |S(x,n,c)| leq C_S $$ with some $C _S > 0$. Systems of this type describe chemotaxis-fluid interaction in cases when the evolution of the chemoattractant is essentially dominated by production through cells. If $m>1$ and $Omegasubset mathbb{R}^2$ 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 and bounded (weak) solution, which significantly improves previous results of several authors. Moreover, the {bf optimal condition} on the parameter $m$ for global existence is obtained. Our approach underlying the derivation of main result is based on an entropy-like estimate involving the functional %Our main tool is consideration of the energy functional $$int_{Omega}(n_{varepsilon} +varepsilon)^{m}+int_{Omega}|nabla c_varepsilon|^{2},$$ where $n_varepsilon$ and $c_varepsilon$ are components of the solutions to (2.1) below." @default.
- W2922367908 created "2019-03-22" @default.
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- W2922367908 date "2019-03-15" @default.
- W2922367908 modified "2023-09-24" @default.
- W2922367908 title "Blow-up prevention by nonlinear diffusion in a 2D Keller-Segel-Navier-Stokes system with rotational flux" @default.
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- W2922367908 doi "https://doi.org/10.48550/arxiv.1903.07536" @default.
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