Lehigh online applied mathematics seminar; topics include but not limited to: differential equations, dynamical systems, fluid dynamics, neuronal networks, numerical simulations, scientific computing, and machine learning. The seminar will generally be scheduled between 9:00am and 12:00pm on Fridays.
All talks will be delivered remotely; please follow this link to all Zoom sessions. If a password is required, please contact the lead seminar organizer Prof. Linghai Zhang for more information.
| The list will be continuously updated and maintained throughout the semester. |
| September 29 (F) - | Zhaosheng Feng (University of Texas Rio Grande Valley) |
| 11:00am-12:00pm | Title: Dynamical behaviors of KdV-Burgers-Kuramoto Equation. |
| Abstract: In this talk, we consider dynamics of a class of the KdV-Burgers-type systems by starting with Burgers-type equations, and then focus on the KdV-Burgers-Kuramoto equation, a partial differential equation that occupies a prominent position in describing some physical processes in motion of turbulence and other unstable process systems. We limit our attention to various wave solutions and their asymptotic behaviors. | |
| October 20 (F) - | Tai-Peng Tsai (University of British Columbia) |
| 11:00am-12:00pm | Title: Gradient estimates for the non-stationary Stokes system with the Navier boundary condition. |
| Abstract: For the non-stationary Stokes system, it is well-known that one can improve spatial regularity in the interior, but not near the boundary if it is coupled with the no-slip boundary condition. In this talk I will show that, to the contrary, spatial regularity can be improved near a flat boundary if it is coupled with the Navier boundary condition with either infinite or finite slip length. The case with finite slip length is more difficult than the case with infinite slip length. This is a joint work with Hui Chen and Su Liang, and is dedicated to Vladimĺr Šverák on the occasion of his 65th birthday.. | |
| October 27 (F) - | Weinan Wang (University of Oklahoma) |
| 10:00am-11:00am | Title: Global well-posedness and the stabilization phenomenon for some two-dimensional fluid equations. |
| Abstract: In this talk, I will talk about some recent well-posedness and stability results for three fluid models in 2D. More precisely, I will discuss the global well-posedness for the 2D Boussinesq equations with fractional dissipation. Furthermore, I will discuss the long-time behavior of solutions. For the Oldroyd-B model, we show that small smooth data lead to global and stable solutions. When Navier-Stokes is coupled with the magnetic field in the magneto-hydrodynamics (MHD) system, solutions near a background magnetic field are shown to be always global in time. The magnetic field stabilizes the fluid. In the examples for Oldroyd-B and MHD, the systems governing the perturbations can be converted to damped wave equations, which reveal the smoothing and stabilizing effect.. | |
| November 3 (F) - | Jingjun Zhang (Jiaxing University) |
| 9:00am-10:00am | Title: Decay estimates of solution to the two-dimensional fractional quasi-geostrophic equation. |
| Abstract: The fractional single-layer quasi-geostrophic equation is considered. We first prove the existence and uniqueness of a smooth solution of the fractional quasi-geostrophic equation by using the regularization method. Then utilizing the Fourier splitting method, we obtain the long-time behavior of the solution. | |
| November 10 (F) - | Yi Du (Jinan University) |
| 09:00am-10:00am | Title: The dispersive behavior to the 3D incompressible MHD with partial dissipation and large data in rotating frame. |
| Abstract: To study the effect of rotation in incompressible magnetohydrodynamics (MHD) flow with partial dissipation, we look at the 3D incompressible MHD equations within a rotating frame with Coriolis force of order 1/ε. Due to the dispersive behavior, the global solution with large initial data to the partial dissipation MHD system was proved when the rotation was fast enough.. | |
| December 1 (F) - | Junping Shi (William & Mary) |
| 11:00am-12:00pm | Title: Modeling animal movement with memory with partial differential equations with time-delay. |
| Abstract: Animal populations often self-organize into territorial structure from movements and interactions of individual animals. Memory is one of cognitive processes that may affect the movement and navigation of the animals. We will review several mathematical approaches of animal spatial movements, and also introduce our recent work using partial differential equations with time-delay to model and simulate the memory-based movement. We will show the bifurcation and pattern formation for such models. It is based on joint work with Chuncheng Wang, Hao Wang, Xiangping Yan, Qingyan Shi and Yongli Song.. |