Global classical solutions in a Keller-Segel(-Navier)-Stokes system modeling coral fertilization

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Li, Xie^1,2 

[1] Chongqing Normal Univ, Sch Math Sci, Chongqing 401131, Peoples R China

[2] Univ Elect Sci & Tech China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

关键词: Chemotaxis;    Keller-Segel;    Navier-Stokes;    Coral fertilization;    Global existence;   

DOI  :  10.1016/j.jde.2019.06.021

来源: Elsevier

【 摘 要 】

This paper is devoted to the coupled Keller-Segel(-Navier)-Stokes system describing coral fertilization: {nt + u center dot del n = Delta n - del center dot (nS(x, n, c)del c) - nm, x is an element of Omega, t > 0, m(t) + u center dot del m = Delta m - nm, x is an element of Omega, t > 0, c(t) + u center dot del c = Delta c - c + m, x is an element of Omega, t > 0, u(t) + kappa(u center dot del)u = Delta u - del p + (n + m)del phi, del center dot u = 0, x is an element of Omega, t > 0, where kappa is an element of {0, 1}, Omega subset of R-N (N = 2, 3) is a bounded domain with smooth boundary partial derivative Omega and outward normal vector nu, the chemotactic sensitivity S(x, n, c) is a tensor valued function satisfying vertical bar S(x, n, c)vertical bar <= S-0(c)/(1+n)(theta) with a non-decreasing function S-0 is an element of C-2([0, +infinity)) and theta >= 0. Under the specified boundary conditions del c center dot nu = del m center dot nu = (del n - nS(x, n, c)del c) center dot nu = 0, u = 0 and some mild assumptions on the initial data (n(0), m(0), c(0), u(0)), the global-in-time classical solutions are constructed. More precisely, if theta > 0, then for any large initial data there admits globally bounded solution; and if theta = 0, under some explicit smallness conditions on max{parallel to c(0)parallel to L-infinity(Omega), parallel to m(0)parallel to L-infinity(Omega)} the global-in-time classical solutions are also constructed. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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