Speaker: Dr. Weinan Wang, Assistant Professor, Department of Mathematics, University of Oklahoma
Date: Wednesday, February 21, 2024, 4:15 – 5:15 PM
Location: Science Engineering Hall (SCEN 403)
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 incompressible fluid equations. More precisely, I will first discuss a global well-posedness result for the 2D Boussinesq equations with fractional dissipation and the long-time behavior of solutions. For the Oldroyd-B model, we show that small smooth data lead to global and stable solutions. When the 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. If time permits, I will discuss some open problems.
Short Bio: Weinan Wang is a first-year Assistant Professor of Mathematics at the University of Oklahoma. He received his Ph.D. in Applied Mathematics under the supervision of Igor Kukavica from the University of Southern California in 2020. He was a Postdoctoral Fellow at the University of Arizona between 2020-2023, and at Mathematical Sciences Research Institute (MSRI) during Spring 2021. His major fields of study are kinetic models, fluid dynamics, electro-chemistry, stochastic PDEs, and mathematical biology. He has published in journals such as Indiana University Mathematics Journal, SIAM Journal on Mathematical Analysis, SIAM Journal on Applied Mathematics, Journal of Evolution Equations, Discrete and Continuous Dynamical Systems, etc.
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