Fall 2020
- Joint talk with A Special Day for Pure Mathematics
Date: Friday, November 20
Time: 6:30 – 7:30 PM
Location: ZOOM
Speaker: Dr. Mihai Tohaneanu (University of Kentucky)
Title: Local energy estimates for the wave equation
Abstract: Local energy estimates are a robust way to measure decay of solutions to linear wave equations. I will discuss several such results on curved backgrounds, including black holes such as Schwarzschild, Kerr, and suitable perturbations, and briefly discuss applications to nonlinear problems. The most challenging geometric feature one needs to deal with is the presence of trapped null geodesics, whose presence yield unavoidable losses in the estimates.
- Joint talk with Department Colloquium
Date: Friday, November 6
Time: 3:30 – 4:30 PM
Location: ZOOM
Speaker: Dr. Weinan Wang (University of Arizona, Tucson)
Title: Persistence of regularity and long time behavior of solutions for the Boussinesq equations
Abstract: We address the global persistence of Sobolev regularity for the 2D fractional Boussinesq equations and then we consider the long time behavior of solutions for the 2D Boussinesq equations in different domains, including the whole space and bounded domain with Lions or Dirichlet boundary conditions.
- Joint talk with Department Colloquium
Date: Friday, September 25
Time: 3:30 – 4:30 PM
Location: ZOOM
Speaker: Dr. Yuanzhen Shao (University of Alabama, Tuscaloosa)
Title: GEOMETRIC AND ANALYTIC ASPECTS OF MULTISCALE SOLVATION MODELS
Abstract: In the past two decades, there has been a tremendous growth of applications of multiscale modeling to fields like material sciences, biology and atmospheric sciences. In this talk, I will discuss several multiscale solvation models. In these models, the solute is described in atomic detail and the solvent is presented as a dielectric continuum. Using tools from minimal surfaces and Calculus of Variation, we study the analytic foundations of the models. In addition, we carefully investigate the geometric properties of the "interface" separating the solute and solvent.
This talk is based on the joint work with Zhan Chen, Elizabeth Hawkins and Kai Wang.