Global Weak Solutions to a Fluid-particle System of an Incompressible Non-Newtonian Fluid and the Vlasov Equation  

作　　者：Pei-yu ZHANG Li FANG Zhen-hua GUO 

机构地区：[1]Department of Mathematics,Northwest University,Xi’an 710127,China [2]School of Mathematics and Information Science&Center for Applied Mathematics of Guangxi,Guangxi University,Nanning 530004,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第4期954-978,共25页应用数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.11931013);Natural Science Foundation of Guangxi(No.2022GXNSFDA035078)。

摘　　要：The purpose of this work is to investigate the existence and uniqueness of weak solutions to the initial-boundary value problem for a coupled system of an incompressible non-Newtonian fluid and the Vlasov equation.The coupling arises from the acceleration in the Vlasov equation and the drag force in the incompressible viscous non-Newtonian fluid with the stress tensor of a power-law structure for p≥11/5.The main idea of the existence analysis is to reformulate the coupled system by means of a so-called truncation function.The advantage of the new formulation is to control the external force term G=-∫Rd(u-v)fdc(d=2,3).The global existence of weak solutions to the reformulated system is shown by using the Faedo-Galerkin method and weak compactness techniques.We further prove the uniqueness of weak solutions to the considered system.

关 键 词：incompressible non-Newtonian fluid Vlasov equation global weak solutions 

分 类 号：O175[理学—数学] O373[理学—基础数学]