# Events for October 17, 2017 from General and Seminar calendars

## Working Seminar in Orbit Equivalence and Measured Group Theory

Time: 10:00AM - 11:00AM

Location: BLOC 624

Title: Stable Actions and Asymptotically Central Sequences I

Abstract: I'll be giving a characterization of stable actions in the sense of Jones-Schmidt using Kida's language of groupoids.

## Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Xin Liu, Texas A&M University

Title: Nonlinear PDEs Seminar

Abstract:
Title: Some gas-vacuum interface problems of compressible Navier-Stokes equations in spherically symmetric motions

Abstract:

I will talk about the well-posedness of two problems concerning the evolution of a flow connected with vacuum. The flow, or gas, connects the vacuum area in a way that the sound speed across the gas-vacuum interface has only Holder continuity. A typical example is the Lane-Emden solution for gaseous stars, where the sound speed is only 1/2-Holder continuity on the gas-vacuum interface. As pointed out by T.P. Liu in 1996, the classical hyperbolic method fails due to such singularity. Only recently, Jang and Masmoudi, Coutand, Lindblad and Shkoller independently developed some weighted energy estimates to show the well-posedness of the inviscid isentropic flows. This work is to investigate how the viscosity will help resolve such singularity. In particular, the equilibrium and the well-posedness of a model based on the thermodynamic model listed in Chandrasekhar’s book (An introduction to the study of stellar structure) is studied. Also, we investigate the global well-posedness of the Navier-Stokes equations, which allows the density and velocity to be large, the gas to connect to vacuum in a general manner but the energy to be small. This is based on my Ph.D. thesis as a student of Prof. Zhouping Xin in the Chinese University of Hong Kong, Hong Kong. ===============

Time: 4:00PM - 5:00PM

Location: BLOC 624

Speaker: Robert Rahm, TAMU

Title: Asymptotic density of eigenvalues for 1 dimensional Schroedinger operators

Abstract: Consider the Schr\odinger Equation -y''(x) + q(x)y(x) = \lambda y(x) on $[0,\infty)$. We will initially assume only that q is non-negative and increasing and \lim_{x\to\infty}q(x) = \infty but will later put some restrictive assumptions on it. We will discuss the asymptotic density of eigenvalues of the equation. In particular, if N(T) is the number of eigenvalues less than T\$ we will show: N(T) = \int_{0}^{q^{-1}(T)}\{T-q(x)\}^{1/2}dx + o(1).

## Student/Postdoc Working Geometry Seminar

Time: 5:00PM - 6:00PM

Location: BLOC 628

Speaker: JM Landsberg, TAMU

Title: Geometry and Strassen's asymptotic sum conjecture

## Sixth Annual Derivative Bee

Time: 7:00PM - 9:00PM

Location: BLOC 149