一类具有低正则初值的趋化–流体耦合模型解的整体存在性  

Global Existence of Solutions for a Chemotaxis-Fluid Coupling Model with Low Regular Initial Data

作　　者：陈娟 韩永杰 

机构地区：[1]西华大学理学院,四川 成都

出　　处：《理论数学》2023年第11期3272-3285,共14页Pure Mathematics

摘　　要：考虑在三维有界区域上带有logistic源的具有信号消耗机制的趋化–流体耦合方程组:的初边值问题,其中Ω⊂ℝ3是一个具有光滑边界的有界区域;n和c满足齐次Neumann边界条件,u满足Dirichlet边界条件;Φ∈W2,∞(Ω);r>0,μ>0,α>1是给定的参数。此前的结果表明:当初值满足n0∈C0(Ω)时,该模型在三维有界凸区域上存在整体弱解。本文进一步研究了当初值条件正则性更低时,该模型弱解的整体存在性。具体而言,初值n0满足n0∈L1(Ω),该模型在三维有界凸区域上存在整体弱解。This paper mainly studies the initial-boundary value problem of chemotaxis-fluid coupling equations with signal consumption mechanism on a three-dimensional bounded domain with logistic source where Ω⊂ℝ3 is bounded domain with smooth boundary;n and c satisfy the homogeneous Neu-mann boundary condition and u satisfy the Dirichlet boundary condition;where Φ∈W2,∞(Ω);where r>0, μ>0, and α>1 are given parameters. Previous results show that the initial value satisfies n0∈C0(Ω), the model has a globally weak solution on the three-dimensional bounded convex region. This paper further examines when the initial value condition regularity is lower, the globally existence of weak solutions in this model. Specifically, the initial value n0 satisfies n0∈L1(Ω), the model has a global weak solution on a three-dimensional bounded convex region.

关 键 词：趋化–流体耦合模型 Logistic源 弱解 

分 类 号：O17[理学—数学]