报告题目1：Some Recent Results on Compressible Navier-Stokes Equations

报告人：李竞研究员，中科院数学与系统科学研究院

报告时间：2025年9月5日（周五）8:30-9:10

报告地点：20-306

报告摘要：The barotropic compressible Navier–Stokes system subject to the Navier-slip boundary conditions in a general two-dimensional bounded simply connected domain is considered. For initial density allowed to vanish, the global existence of strong and weak solutions is established when the shear viscosity is a positive constant and the bulk one proportional to a power of the density with the power bigger than one and a third. It should be mentioned that this result is obtained without any restrictions on the size of initial value. To get over the difficulties brought by boundary, on the one hand, Riemann mapping theorem and the pull-back Green's function method are applied to get a pointwise representation of the effective viscous flux. On the other hand, since the orthogonality is preserved under conformal mapping due to its preservation on the angle, the slip boundary conditions are used to reduce the integral representation to the desired commutator form whose singularities can be cancelled out by using the estimates on the spatial gradient of the velocity.

报告人简介：李竞，研究员，中科院数学与系统科学研究院，主要研究方向为可压缩Navier-Stokes方程，李竞研究员证明了三维空间可压缩Navier-Stokes方程含真空的大震荡古典解的整体存在性等一系列重要结果，其研究工作发表在国际著名数学杂志《Comm. Pure Appl. Math.》、《Arch. Ration. Mech. Anal.》、《Ann PDE》、《Comm. Math. Phys.》、《J. Math. Pures Appl.》和《SIAM J. Math. Anal.》等。

报告题目2：Geometric Effects on Geophysical Fluid Dynamics

报告人：杜毅教授，暨南大学

报告时间：2025年9月5日（周五）9:20-10:00

报告地点：20-306

报告摘要：This presentation explores the profound influence of geometric complexities on geophysical fluid dynamics. First, we investigate The Ekmman boundary layer phenomena in Earth's fluid systems with non-flat boundaries, analyzing how topographic variations significantly alter classical boundary layer theory and affect large-scale geophysical flows. Second, we examine the stability properties of non-flat vortex sheets, demonstrating that geometric curvature fundamentally modifies the classical Kelvin-Helmholtz instability paradigm and introduces new stabilization mechanism. Our analysis reveals that curved vortex interfaces exhibit enhanced stability characteristics compared to their planar counterparts, with important implications for atmospheric and oceanic flow patterns. The mathematical framework combines asymptotic analysis of boundary layers with spectral stability theory for curved interfaces, providing new insights into the interplay between geometry and fluid stability in geophysical contexts.

报告人简介：杜毅，暨南大学，2007年博士毕业于复旦大学，后于中山大学从事博士后工作。于2009年入职华南师范大学，历任讲师，副教授，并于2014年被评为教授。2016年9月调入暨南大学信息科学技术学院数学系，任教授至今。主要研究方向为：基础数学偏微分方程领域的非线性色散方程、流体力学方程组等，目前发表科研论文40余篇，均为SCI收录，部分发表在《Comm. P.D.E.》、《J.Math Pure Appl.》、《SIAM J.M.A.》、《J.D.E》等本专业权威期刊。曾在2019年入选暨南大学双百英才；曾主持并完成国家自然科学基金四项，省部级项目四项；参与国家重点研发项目一项。

报告题目3：Kinetic modeling on collective behavior of active particles

报告人：廖杰教授，上海财经大学

报告时间：2025年9月5日（周五）10:10-10:50

报告地点：20-306

报告摘要：Different from classical particles like molecules or atoms, active particles have certain activities, perform specific strategies, interact (rather than collide) with others and the environment, and sometimes can even consume energy to generate motion out of equilibrium. This talk provides a comprehensive journey through the kinetic modeling approach, which serves as the crucial mesoscopic bridge connecting microscopic particle dynamics to macroscopic hydrodynamic theories.  It transfers the dynamics of interactions at the small scale of individuals into the collective behavior of the complex living systems. In this talk, I will review the basic concepts and some applications of this approach.

报告人简介：廖杰，上海财经大学，研究方向：偏微分方程尤其是动理学方程的建模与分析，近期的研究工作主要是广义动理学方程在人群动力学、演化经济学等学科中的应用。

报告题目4：Jeffery-Hamel flows in a 2D sector

报告人：王云教授，苏州大学

报告时间：2025年9月5日（周五）11:00-11:40

报告地点：20-306

报告摘要：We will talk about the self-similar solutions of the steady Navier-Stokes system in a two-dimensional sector with the no-slip boundary condition. We give necessary and sufficient conditions in terms of the angle of the sector and the flux of the flow to guarantee the existence of self-similar solutions of a given type. We also investigate the uniqueness and non-uniqueness of flows with a given type.  As a consequence of the classification of self-similar solutions in the half-space, we characterize the leading order term of the steady Navier-Stokes system in an aperture domain when the flux is small.

报告人简介：王云，苏州大学教授，博士毕业于香港中文大学。主要研究领域为不可压缩流的适定性问题，特别是非齐次不可压方程与管道流问题。曾多次主持国家自然科学基金项目，发表论文20多篇，部分论文发表在《CMP》、《ARMA》、《M3AS》、《MATH ANNALEN》等杂志上。

报告题目5：Global classical solutions to the full compressible Navier-Stokes equation with slip boundary conditions

报告人：吕博强教授，南昌大学

报告时间：2025年9月5日（周五）11:50-12:30

报告地点：20-306

报告摘要：This talk concerned with the initial-boundary-value problem of the full compressible Navier-Stokes system with Navier-slip boundary conditions on the velocity and Neumann boundary one on the temperature in a three-dimensional simply connected bounded smooth domain. We establish the global existence of the classical and weak solutions, under the condition that the initial total energy is suitably small. It should be noted that the initial density and temperature are allowed to vanish. Moreover, for the classical solutions, the exponential decay rates at large time of the density, velocity, and temperature are described.

报告人简介：吕博强，南昌大学教授、博士生导师，江西省省级人才，兼任江西省数学学会副理事长。主要从事流体力学方程的数学理论研究，相关研究结果发表在《Arch. Rational Mech. Anal.》、《J.Math. Pures Appl.》、《Indiana Univ. Math. J.》、《Nonlinearity》等期刊；主持国家自然科学基金4项（面上2项，青年、天元各1项）、江西省自然科学基金3项、中国博士后基金一等资助1项。

邀请人：流体与色散方程的分析创新团队