10月17日上午：8:30-12:00

1.报告题目：On the Initial-Boundary-Value Problem for a Compressible Oldroyd-B Model

摘要：We study the initial-boundary-value problem for a compressible

Oldroyd-B model with zero retardation in the half-space . Following the slip boundary conditions commonly used for the classical Navier-Stokes equations, we formulate a set of boundary conditions suitable for this system. We then establish that the linearized system is globally well-posed in H^1  without requiring any smallness assumption on the initial data. Interestingly, we also show that the linearized system is not well-posed in H^k for any k\geq 2. This work provides the first investigation of  the compressible Oldroyd-B model in the presence of a boundary.

报告人简介：琚强昌，北京应用物理与计算数学研究所研究员，博士生导师。研究领域为可压缩流体力学方程的数学理论，研究工作发表在Adv. Math.、 ARMA、CMP 和JMPA 等国际权威学术期刊上。

2.报告题目：Vanishing viscosity limit toward rarefaction wave with vacuum for the two-fluid Navier-Stokes-Poisson system

摘要：We study the vanishing viscosity limit toward rarefaction waves with vacuum for the two-fluid Navier-Stokes-Poisson system. Starting from a one-sided vacuum rarefaction wave of the quasineutral Euler system, we construct corresponding viscous solutions and prove their uniform convergence to the Euler rarefaction wave as the viscosity coefficients vanish. The analysis reveals the behavior of the two distinct densities near the vacuum state under different viscosity coefficients. Moreover, we establish an explicit uniform convergence rate from the two-fluid Navier-Stokes-Poisson system to the corresponding quasineutral Euler equations in the vanishing viscosity limit.

报告人简介：姚磊，西北工业大学教授，博士生导师，主要从事流体力学中的偏微分方程数学理论的研究，论文发表在Math.Ann.、JMPA、Ann.I.H.Poicaré-AN、SIAM J. Math. Anal.、Indiana Univ. Math. J.、M3AS等国际期刊上。

3.报告题目：Optimal convergence rates of the Klein- Gordon- Schrödinger systemin the nonrelativistic limit

摘要：In this paper, we study the Klein-Gordon-Schrödinger system in the nonrelativistic regime $\e \to 0$, where $\e$ is proportional to the inverse of the speed of light. For initial data with limited regularity, we show that the Klein-Gordon-Schrödinger system converges to a system of decoupled linear Schrödinger equations over a long time interval of order $\e^{-1}$ with error estimates of the form $(1+t)\e^2$. For more regular initial data,  we show the convergence and error estimates hold for a longer time interval of order $\e^{-\frac{4}{3}}$, where the error estimate for the Schr\"odinger component can be improved to $(1 + \e t + \e^2 t^2)\e^2$.  The specific forms of the error estimates coincide with the numerical results in \cite{BZ17}, and the $O(\e^{2})$ convergence rates coincide with the order of initial error, and thus are optimal.

报告人简介：吕勇，南京大学教授，博士生导师。研究领域是偏微分方程的稳定性分析和渐近分析，相关研究成果发表在Mem. EMS、Math. Ann.、ARMA、SIAM J. Math. Anal.、CVPDE等期刊上。

4.报告题目：Dynamical stability of steady solution to unsteady radially symmetric Euler-Poisson flow with nonzero angular velocity.

摘要：In this talk, we will introduce some results about the two-dimensional radially symmetric unsteady Euler-Poisson flows with nonzero angular velocity in an annulus. We first give the smooth steady solutions in subsonic, supersonic regimes. Moreover, for the steady supersonic steady solutions, we establish global stability for the corresponding unsteady radially symmetric Euler-Poisson system. Furthermore, under the time-periodic boundary conditions in inlet, we show the result that the classical solution is also time-periodic.

报告人简介：刘见礼，上海大学教授，博士生导师，从事应用偏微分方程理论与应用研究，在IMRN、JDE、 Nonlinearity、CVPDE等国际知名期刊发表论文40余篇。

10月17日下午：14:00-17:30

5.报告题目：Sharp non-uniqueness of weak solutions to the semilinear wave equation

摘要：In this talk, we would discuss a non-uniqueness result to the semilinear wave equation

\[ \partial_{tt}u-\partial_{xx}u= \Theta_1(\partial_t u)^2 + \Theta_2(\partial_x u)^2.\] For any $\Theta_1 \Theta_2 < 0$, $\beta<1$, we construct infinitely many weak solutions $u \in C_{t,x}^{\beta}$ with zero initial data. The construction is based on a frequency-localized convex integration scheme. Together with the classical local uniqueness theory in \(C_{t,x}^{1}\), this non-uniqueness result is sharp.

报告人简介：曲鹏，复旦大学教授，博士生导师。主要从事应用偏微分方程的数学研究，在双曲守恒律、流体力学方程弱解等方面取得的成果发表在 Adv. Math.、ARMA、JMPA 等国际知名期刊。

6.报告题目：Wave breaking for a hyperbolic-elliptic coupled system in three dimensions

摘要：This talk focuses on wave breaking for a hyperbolic-elliptic coupled system in three dimensions. At the blow-up, the solution is smooth except at a single point, where it features a cusp-type singularity. Moreover, in self-similar variables, the solution converges asymptotically to the steady profile of the corresponding three-dimensional self-similar Burgers equation.

报告人简介：王跃循，首都师范大学教授，博士生导师，其主要研究兴趣为可压缩流体力学偏微分方程的适定性和色散偏微分方程的波的破裂以及动力学行为，相关研究成果发表于ARMA、CPDE、Math. Ann、M3AS、SIMA等数学期刊。

7.报告题目：Global existence and asymptotics for nonlinear elastic waves

摘要：For the Cauchy problem of nonlinear elastic wave equations of three-dimensional isotropic, homogeneous and hyperelastic materials satisfying the null condition, global existence of classical solutions with small initial data was proved in Agemi (Invent Math 142:225-250, 2000) and Sideris (Ann Math 151:849-874, 2000), independently. In this talk, we will give an alternative proof for the global existence result. Then based on this new proof, we will also clarify the asymptotic behavior of global solutions.

报告人简介：查冬兵，东华大学教授，博士生导师。研究方向为非线性偏微分方程，尤其是双曲型方程的分析理论。相关研究论文发表于 JMPA、JFA、CVPDE、ESAIM: COCV、JDE等国际知名数学杂志。

8.报告题目：Hardy space and exponential decay of 2D inhomogeneous incompressible flows

摘要：In this talk, we investigate the 2D Cauchy problems of inhomogeneous incompressible Navier-Stokes equations. The central issue is to identify the far field state of the velocity and control the remainder. To get over the difficulties caused by vacuum and critical Sobolev embedding, we apply the cancellation structure inherent in the 2D equations and establish weighted estimates at endpoint to recover the global bound of velocity. In such process, Hardy space provides the proper analysis framework to capture the mechanism. As the application of above argument, we obtain the global exponential decay of solution and uniform-in-time regularity of flow maps for general initial density including the measurable density patches.

报告人简介：樊心宇，南开大学副教授。博士毕业于中国科九游体育数学与系统科学研究院，先后于北京应用物理与计算数学研究所、中科院九游体育从事博士后研究，主要研究流体力学偏微分方程，成果发表于 ARMA、JDE 等期刊。

报告地点：九游体育301报告厅