Global classical solutions in chemotaxis(-Navier)-Stokes system with rotational flux term
Global classical solutions in chemotaxis(-Navier)-Stokes system with rotational flux term
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DOI：
10.1016/j.jde.2016.09.007
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发表时间：
2016-12-15
影响因子：
2.4
通讯作者：
Cao, Xinru
中科院分区：
文献类型：
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作者：
Cao, Xinru
耦合趋化流体系统(n(t) = Delta n - del . (nS(x,n,c) . del(C)) - u .del n, (x,t) 是 Omega x (0, T) 的一个元素,c(t) = Delta c - nc - u .del(C), (x, t) 是 Omega x (0, T) 的一个元素,u(t) = Delta u - k(u del)u + del P + n del phi, (x,t) 是 Omega x (0, T) 的元素，del u = 0，(x,t) 是 Omega x (0, T) 的元素，(*) 在 R-N 有界光滑域 Omega 子集 (N = 2,3) 上考虑 n、c 的无通量边界条件和 u 的狄利克雷边界条件。我们假设 S(x, n, c) 是一个温和假设下的矩阵值敏感度，使得垂直条 S(x, n, c)垂直条 < S-0(c(0)) 以及一些非递减函数 S-0 是 C-2((0, 无穷大)) 的元素。与相关标量敏感度情况相比，(*) 不具有自然梯度函数结构。在目前的工作中，在平行于 C-0 平行于（L 无穷大（Omega））的小假设下构建了全局经典解，此外，我们获得了该解的有界性和大时间收敛性，这意味着化学力的初始浓度较小。保留所有权利。
The coupled chemotaxis fluid system(n(t) = Delta n - del . (nS(x,n,c) . del(C)) - u . del n, (x,t) is an element of Omega x (0, T),c(t) = Delta c - nc - u . del(C), (x, t) is an element of Omega x (0, T),u(t) = Delta u - k(u . del)u + del P + n del phi, (x,t) is an element of Omega x (0, T),del . u = 0, (x,t) is an element of Omega x (0, T), (*)is considered under the no-flux boundary conditions for n, c and the Dirichlet boundary condition for u on a bounded smooth domain Omega subset of R-N (N = 2,3), k is an element of{0,1}. We assume that S(x, n, c) is a matrix-valued sensitivity under a mild assumption such that vertical bar S(x, n, c)vertical bar < S-0(c(0)) with some non-decreasing function S-0 is an element of C-2((0, infinity)). It contrasts with the related scalar sensitivity case that (*) does not possess the natural gradient-like functional structure. Associated estimates based on the natural functional seem no longer available. In the present work, a global classical solution is constructed under a smallness assumption on parallel to C-0 parallel to(L infinity(Omega)) and moreover we obtain boundedness and large time convergence for the solution, meaning that small initial concentration of chemical forces stabilization. (C) 2016 Elsevier Inc. All rights reserved.