Event Detail

Event Type: 
Department Colloquium
Tuesday, February 19, 2013 - 06:00 to 07:00
Kidder 350

Speaker Info

Carnegie Mellon University

The evolution of the velocity field of incompressible fluids is governed by the Navier-Stokes equations. The pressure term in these equations has been a constant source of difficulty in numerics and theory like. Formally, it is a Lagrange multiplier used to enforce the incompressibility constraint. Yet the pressure gradient has "physical meaning" (force per unit area) and propagates with infinite speed.

Most of what I will talk about is motivated by the analysis of a numerical scheme for incompressible fluids. The main idea (dating back to Johnston-Liu '04) was to replace the incompressibility constraint with an explicit equation for the pressure, in an attempt to produce an efficient and accurate numerical scheme. While this successfully address some issues, it makes some analytical questions much harder. I will briefly address a few resolved, and unresolved analytical questions related to existence and regularity for this system.