三维非齐次不可压缩Navier-Stokes-Vlasov方程组在移动区域上弱解的整体存在性  

Global existence of solutions to the three-dimensional nonhomogeneous incompressible Navier-Stokes-Vlasov equations in a time-dependent domain

作　　者：张师豪 王丽真[1,2] ZHANG Shihao;WANG Lizhen(Nonlinear Studies of Science, Northwest University, Xi′an 710127, China;School of Mathematics, Northwest University, Xi′an 710127, China)

机构地区：[1]西北大学非线性科学研究中心,陕西西安710127 [2]西北大学数学学院,陕西西安710127

出　　处：《西北大学学报（自然科学版）》2022年第2期288-297,共10页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金(11771352,11871396);陕西省自然科学基金(2020JM-431)。

摘　　要：文中考虑了三维非齐次不可压缩Navier-Stokes-Vlasov方程组在移动区域上弱解的整体存在性,此结果是将文献[7]中齐次不可压缩情形推广到非齐次不可压缩情形。假设流体的初始密度有下界,基于Schaefer不动点定理和弱收敛方法证明了三维非齐次不可压缩Navier-Stokes-Vlasov方程组在移动区域上弱解的整体存在性。In this paper,we consider the global existence of weak solutions of three-dimensional nonhomogeneous incompressible Navier-Stokes-Vlasov equations in a time-dependent domain.The global existence results of weak solutions of homogeneous incompressible Navier-Stokes-Vlasov equations in literature[7]are generalized,and on the promise that the initial density of the fluid has a lower bound,the global existence of solutions to the three-dimensional nonhomogeneous incompressible Navier-Stokes-Vlasov equations in a time-dependent domain is obtained by using Schaefer′s fixed point theorem and the weak convergence method.

关 键 词：三维非齐次不可压缩Navier-Stokes-Vlasov方程组 Schaefer不动点定理 弱收敛方法 

分 类 号：O175.2[理学—数学]