具有粗糙密度场的三维非均质不可压缩非对称流体弱解的唯一性  

The Uniqueness of Weak Solution for 3D Incompressible Inhomogeneous Asymmetric Fluids with Only Rough Density

作　　者：王晓杰 徐夫义 Xiaojie Wang;Fuyi Xu(School of Mathematics and Statistics,Shandong University of Technology,Zibo 255049,P.R.China)

机构地区：[1]山东理工大学数学与统计学院,淄博255049

出　　处：《数学学报(中文版)》2025年第2期211-223,共13页Acta Mathematica Sinica:Chinese Series

基　　金：国家自然科学基金(11501332,11771043,51976112,12326430);山东省自然科学基金(ZR2021MA017)。

摘　　要：本文主要研究具有粗糙密度场的三维非均质不可压缩非对称流体的柯西问题.通过开发一些解关于时间额外的加权估计,运用插值理论和关于时间变量的Lorentz空间的相关性质,建立了速度场的Lipschitz正则性.基于此,采用对偶方法,获得了由[Qian,Chen and Zhang,Math.Ann.,2023,386:1555-1593]构造的整体弱解的唯一性.The present paper is dedicated to the study of the Cauchy problem for 3D incompressible inhomogeneous asymmetric fluids with only rough density.By exploiting some extra time-weighted energy estimates,and employing the interpolation argument and Lorentz norms for the time variable,we first construct the Lipschitz regularity of the velocity.Based on it,following the duality approach,we finally settle the uniqueness issue of the global weak solution constructed by[Qian,Chen and Zhang,Math.Ann.,2023,386:1555-1593].

关 键 词：唯一性 非均质非对称流体 粗糙密度场 

分 类 号：O175.2[理学—数学]