讲座题目一：The incompressible jet flow with vorticity and gravity

讲座摘要：This talk is concerned with the well-posedness theory and geometric property of steady incompressible jet flow with vorticity and gravity. The main results show that for given incoming mass flux and atmospheric pressure at outlet there exists a unique smooth incompressible jet flow issuing from a semi-infinitely long nozzle. Moreover, we obtain the single intersection property and monotonicity of the free boundary.

讲座时间：2024年4月13日（周六）上午9:00

讲座地点：综合楼806会议室

嘉宾简介：程建峰，四川大学数学学院教授、博士生导师，主要从事非线性偏微分方程的研究工作，在Arch. Rational Mech. Anal.、Trans. AMS、Calc. Var. PDEs等发表论文10余篇。入选2021年度教育部重要人才计划青年学者，主持国家重点研发计划青年科学家项目和国家自然科学基金项目。

讲座题目二：Wave breaking to the Whitham type equation

讲座摘要：We will report some recent wave breaking results to the Whitham type equation. This talk is based on the joint works with C. Klein, J.-C. Saut, S. Sun and Y. Zhang.

讲座时间：2024年4月13日（周六）上午10:00

讲座地点：综合楼806会议室

嘉宾简介：王跃循，兰州大学数学与统计学院教授，博导，国家特聘青年专家。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。

讲座题目三：Vanishing capillarity limit of the 3D isentropic compressible Navier-Stokes-Korteweg equations in a slab domain

讲座摘要：In this talk, we consider the global well-posedness of the isentropic compressible Navier-Stokes-Korteweg (NSK) equations in conormal Sobolev spaces in the domain T^2×[0,1], where the velocity satisfies slip boundary condition and the density is supplemented with Neumann boundary condition. Moreover, we establish the uniform estimates of the global strong solution with respect to the capillarity coefficient. Based on the uniform estimates, we prove that the strong solution of the isentropic compressible NSK equations converges globally in time to the strong solution of the isentropic compressible Navier-Stokes equations as the capillarity coefficient tends to zero.

讲座时间：2024年4月13日（周六）上午11:00

讲座地点：综合楼806会议室

嘉宾简介：张志朋，中国海洋大学副教授，主要研究流体力学方程组及相关模型的小参数极限理论与毛细流体中的Rayleigh-Taylor不稳定性问题，现已在SIAM、CVPDE、Nonlinearity等国际知名学术期刊上发表论文十余篇。