报告时间：2025年9月4日（星期四）9：00-17：00

报告地点：数学科学学院208会议室

报告人及报告简介：

报告人：SCHINDLER Jule Antonia（Doctor of the University of Erlangen-Nuremberg）

报告题目：The Euler equations and the problem about weak solutions

报告摘要：Motivated by the modeling of turbulent flows, we introduce the Euler equations and discuss some results on the full space in two and three dimensions. We will investigate the problem of deriving weak solutions as a limit of Leray weak solutions of Navier-Stokes with vanishing viscosity. At the end, we provide an insight into the concept of very weak solutions and finally into my own research project.

报告人：ŠKONDRTĆ Stefan（Doctor of the University of Erlangen-Nuremberg）

报告题目：Relative energy method for weak-strong uniqueness for the Navier-Stokes equations

报告摘要：In this talk we discuss the relative energy method for weak-strong uniqueness for the Navier-Stokes equations. After recalling some classical results for the Navier-Stokes equations with constant density, we discuss the existence and uniqueness of weak solutions for the Navier-Stokes with variable density in two space dimensions.

报告人：Schröder Jens（Doctor of the University of Erlangen-Nuremberg）

报告题目：On the Vanishing Viscosity Limit for Inhomogeneous Incompressible Navier-Stokes Equations on Bounded Domains

报告摘要：In this talk we study the vanishing viscosity limit for the inhomogeneous incompressible Navier Stokes equations on bounded domains with no-slip boundary condition in two or three space dimensions. First, we make a few general remarks about the Navier-Stokes and Euler equations and explain the differences between the two models and the importance of the viscosity. Then, we explain the class of solutions that we are working with and sketch Kato’s criterion for homogeneous Navier-Stokes equations. We introduce the key ideas of the relative energy method. Using the relative energy method together with suitable assumptions on the density, we establish the convergence in energy space of Leray-Hopf type solutions of the Navier-Stokes equation to a smooth solution of the Euler equations if and only if the energy dissipation vanishes on a boundary layer with thickness proportional to the viscosity. This extends Kato’s criterion for homogeneous Navier-Stokes equations to the inhomogeneous case.

报告人：DEMMEL Josef Felix（Doctor of the University of Erlangen-Nuremberg）

报告题目：An introduction to the Navier-Stokes equations

报告摘要：The goal of the talk is to introduce the Leray-Hopf framework for the homogenous,incompressible Navier-Stokes equations.We begin with formal manipulations to derive the funda mental energy balance and to explain the role of the pressure term. Next, we formulate the notion of weak (Leray–Hopf) solutions and give an overview about the key results,contrasting the two- and three-dimensional case.

报告人：寿凌云（南京师范大学）

报告题目：Convergence to equilibrium states in Vlasov-Navier-Stokes flows

报告摘要：We investigate large-time dynamics for finite-energy weak solutions of Vlasov-Navier-Stokes equations in a two-dimensional torus. We first consider the homogeneous case where the incompressible, viscous fluid coupled with the particles has a constant density, and then study the variable-density case. In both cases, we establish the large-time convergence of the distribution function to the monokinetic state. More precisely,  for incompressible Vlasov-Navier-Stokes equations with finite-energy initial data,  we exhibit an algebraic time convergence rate of the global weak solution, deteriorating as the initial particle distribution increases. If the initial particle distribution is sufficiently small, the convergence rate becomes exponential, a result consistent with the work of Han-Kwan et al. (2020) dedicated to the homogeneous, three-dimensional case, where an additional smallness condition on the velocity was required. Furthermore, in the non-homogeneous case, we establish similar stability results, allowing a piecewise constant fluid density with jumps. This work is a joint collaboration with Prof. Raphaël Danchin.

主办单位：扬州大学数学学院

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