School of Mathematics

The inviscid limit for the Navier-Stokes equations with data analytic only near the boundary

Fei Wang
University of Maryland
May 30, 2019

We address the inviscid limit for the Navier-Stokes equations in a half space, with initial datum that is analytic only close to the boundary of the domain, and has finite Sobolev regularity in the complement. We prove that for such data the solution of the Navier-Stokes equations converges in the vanishing viscosity limit to the solution of the Euler equation, on a constant time interval.

Uniform Rectifiability via Perimeter Minimization IV

Tatiana Toro
University of Washington
May 24, 2019

Abstract: Quantitative geometric measure theory has played a fundamental role in the development of harmonic analysis, potential theory and partial differential equations on non-smooth domains. In general the tools used in this area differ greatly from those used in geometric measure theory as it appears in the context of geometric analysis. In this course we will discuss how ideas arising when studying perimeter minimization questions yield interesting and powerful results concerning uniform rectifiability of sets. The course will be mostly self-contained.

Uniform Rectifiability via Perimeter Minimization III

Tatiana Toro
University of Washington
May 23, 2019

Abstract: Quantitative geometric measure theory has played a fundamental role in the development of harmonic analysis, potential theory and partial differential equations on non-smooth domains. In general the tools used in this area differ greatly from those used in geometric measure theory as it appears in the context of geometric analysis. In this course we will discuss how ideas arising when studying perimeter minimization questions yield interesting and powerful results concerning uniform rectifiability of sets. The course will be mostly self-contained.

Ancient Solutions to Geometric Flows III

Panagiota Daskalopoulos
Columbia University
May 23, 2019

Abstract: Some of the most important problems in geometric evolution partial differential equations are related to the understanding of singularities. This usually happens through a blow up procedure near the singularity which uses the scaling properties of the equation. In the case of a parabolic equation the blow up analysis often leads to special solutions which are defined for all time −∞

Ancient Solutions to Geometric Flows

Panagiota Daskalopoulos
Columbia University
May 21, 2019

Abstract: Some of the most important problems in geometric evolution partial differential equations are related to the understanding of singularities. This usually happens through a blow up procedure near the singularity which uses the scaling properties of the equation. In the case of a parabolic equation the blow up analysis often leads to special solutions which are defined for all time −∞

Uniform Rectifiability via Perimeter Minimization II

Tatiana Toro
University of Washington
May 21, 2019

Abstract: Quantitative geometric measure theory has played a fundamental role in the development of harmonic analysis, potential theory and partial differential equations on non-smooth domains. In general the tools used in this area differ greatly from those used in geometric measure theory as it appears in the context of geometric analysis. In this course we will discuss how ideas arising when studying perimeter minimization questions yield interesting and powerful results concerning uniform rectifiability of sets. The course will be mostly self-contained.

Uniform Rectifiability via Perimeter Minimization

Tatiana Toro
University of Washington
May 20, 2019
Abstract: Quantitative geometric measure theory has played a fundamental role in the development of harmonic analysis, potential theory and partial differential equations on non-smooth domains. In general the tools used in this area differ greatly from those used in geometric measure theory as it appears in the context of geometric analysis. In this course we will discuss how ideas arising when studying perimeter minimization questions yield interesting and powerful results concerning uniform rectifiability of sets. The course will be mostly self-contained.