一类具有低正则初值的趋化-流体耦合模型的弱可解性

Global Weak Solvability for a Chemotaxis-Fluid Model with Low Regular Initial Data

考虑二维有界区域上带有logistic源的趋化-流体耦合方程组初边值问题。本文证明了当初值仅为可积函数时,该模型弱解的整体存在性。具体而言:当r≥0,μ> 0时,对于任意的α≥2,初值n_(0)∈L^(1)(Ω),该模型在二维有界区域中存在整体弱解。

We study the initial-boundary value problem of two-dimensional Chemotaxis-fluid coupling system with logistic term This paper proves that the global existence of weak solution of system exists when the initial data are only integrable functions.More precisely,it is proved that under the assumption that,for any and the initial value belongs to L^(1)(Ω),the above system admits a global weak solution.