报告题目：Existence and partial regularity of suitable weak solutions to the 3D-Navier-Stokes-Vlasov-Fokker-Planck equations

报告人：于锏博 大连理工大学

报告时间：2026年06月27日10:50-11:20

报告地点：腾讯会议ID 609-2797-9994

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校内联系人：徐佳宁[email protected]

报告摘要：

    In this paper, we investigate the incompressible Navier-Stokes equations coupled with the Vlasov-Fokker-Planck equation, which describes a two-phase mixture of the viscous incompressible fluid with particles or bubbles through a frictional force term. In the three-dimensional whole space, we construct a new class of suitable weak solutions to the Navier-Stokes-Vlasov-Fokker-Planck system satisfying energy estimates and three local or global energy inequalities of different forms. These obtained local energy inequalities play an important role in characterizing the measure of the singularity set of weak solutions. The main difficulties in deriving these inequalities lie in establishing the convergence of the density function $f$ in bounded or unbounded domains and dealing with the convergence of the non-local frictional force term. The strong convergence of both $f$ and $f\log f$ weighted by $|v|^k$ is proved by exploring some new a priori quantities of the velocity with the help of Tao's $L^p$ decomposition and the DiPerna-Lions compactness method. Moreover, as an immediate consequence of the existence result, we are able to describe the Hausdorff dimension of set of singular points of the fluid velocity $u$ and also establish the $\alpha$ -Hölder continuity of $f$ at the regular points of $u$ .

报告人简介：

    于锏博，大连理工大学数学科学学院博士，本硕毕业于A片 ，主要研究领域包括Navier-Stokes方程，MHD方程及趋化方程的适定性及正则性，以及动力学方程的正则性。目前有关Navier-Stokes方程的强解存在性结果发表在《Journal of Geometric Analysis》。