2025偏微分方程会议

活动主题

2025偏微分方程学术会议

简历

（外籍人士需提供中文简历）

报告题目

Data assimilation algorithms for the three dimensional planetary geostrophic equations of large-scale ocean circulation

报告

主要观点

In this talk, we consider data assimilation algorithms for the three dimensional planetary geostrophic equations of large-scale ocean circulation in the case that the observable measurements, obtained continu- ous/discretely in time, which works for a general class of observable measurements, such as low Fourier modes and local spatial averages over finite volume elements. We will provide some suitable conditions to establish asymptotic in time estimates of the difference between the approximating solution and the unknown exact (reference) solution in some appropriate norms for some different kinds of interpolant operators, which also shows that the approximation solution of the proposed data assimilation algorithm will convergent to the unique unknown exact solution of the original system at an exponential rate asymptotically in time.

主讲人照片

简历

梅钰，西北工业大学，副教授。2016年博士毕业于香港中文大学。2016年至2020年分别在澳大利亚昆士兰大学和意大利格兰萨索科学研究所从事博士后研究。主要从事非线性偏微分方程，特别是流体动力学方程方面的研究，具体研究兴趣为可压缩Navier-Stokes 及磁流体方程组适定性，可压缩流体自由边值问题的适定性与渐近极限，液晶流方程的适定性。研究结果发表在Adv. Math, M3AS,CVPDE,SIMA,Sci.China Math.等学术期刊上。

报告题目

On three-dimensional liquid crystal flows with general elastic energy

报告

主要观点

In this talk, we present some results on the well-posedness and singular limits of three-dimensional liquid crystal flows with general elastic energy. For the Ericksen-Leslie system, we proved the existence and uniqueness of local strong solutions and smooth convergence up to the maximal existence time from the local solutions to the Ginzburg-Landau approximation. For the Beris-Edwards system, we obtained the local strong solutions to both biaxial and uniaxial Q-tensor flows, and justified the large body limits from biaxial to uniaxial Q-tensor flows. These are joint works with Dr. Zhewen Feng and Prof. Min-Chun Hong from University of Queensland, Australia.

主讲人照片

简历

杨佳琦，副教授，博士生导师。博士毕业于南京大学数学系，随后在中科院力学研究所从事博士后研究。研究方向是非线性偏微分方程与流体力学中的数学理论，主要关注不可压缩牛顿与非牛顿流体力学方程组的适定性理论以及流体力学方程组中的自由边值问题。在SIAM J. Math. Anal., Calc. Var. Partial Differential Equations, Nonlinearity, Phys. D, Sci. China Math., J. Differential Equations等期刊上发表多篇论文。

报告题目

Some results on the stationary Navier-Stokes equations in a pipe or (convergent) channel

报告

主要观点

In this talk, I will present recent advances in Leray's problem for the 3D/2D stationary Navier-Stokes equations in infinitely long pipes/channels with Navier-slip boundary conditions. I will also introduce a uniqueness result for the solution (Landau-Lifschitz solution) to the 2D stationary Navier-Stokes equations in an infinitely long convergent channel.

主讲人照片