S4B1 - Graduate Seminar in Analysis and PDEs - Topics in Incompressible Fluid Dynamics

Summer term 2023

Dr. Dimitri Cobb

Organisational details

Overview

This seminar series are centered on the study of the Euler and Navier-Stokes equations, and the properties of their solutions. We will first start by covering the classical question of existence and uniqueness of solutions for a given initial datum. This will involve getting familiar with important tools from harmonic analysis. However, the analysis of these PDEs goes much deeper than the (already fascinating) existence/uniqueness problems: we will also examine some important properties of the solutions. For example, we will study the asymptotic behavior of solutions at large space scales, mixing properties and the growth of higher order norms, point vortex dynamics, or the distribution of kinetic energy in the solutions. Other related models such as magnetohydrodynamics will also recieve some attention.

See here for more information, including a list of literature recommendations.

Prerequisites: basic knowledge of Fourier series and transform, functional analysis, Sobolev spaces and ODEs. No prior experience in physics is required.

Schedule of talks

October 10- Talk 01 TBA

October 17- Talk 02 TBA

October 24- Talk 03 TBA

October 31- Talk 04 TBA

November 7- Talk 05 TBA

November 14- Talk 06 TBA

November 21- Talk 07 TBA

November 28- Talk 08 TBA

December 5- Dies Academicus

December 12- Talk 09 TBA

December 19- Talk 10 TBA

December 19- Talk 11 TBA

December 26- Christmas break

January 2- Christmas break

January 9- Talk 12 TBA

January 16- Talk 13 TBA

January 23- Talk 14 TBA