Department of Mathematics


Upcoming Colloquiums

Location: Surge 284

Time: 4:10 - 5:00pm

Light Refreshments Served

March 14, 2008

Dr. James Kelliher

Brown University

"Vanishing Viscosity in the Presence of a Boundary"

The behavior of an incompressible fluid as we let its viscosity approach zero is poorly understood when a boundary is present. Understanding this behavior is of both theoretical and practical interest. The most natural question to ask is whether in this
vanishing viscosity limit solutions to the Navier-Stokes equations, which describe an incompressible viscous fluid, converge in the energy norm to a solution to the Euler equations, which describe an incompressible inviscid fluid. Under the assumption that the viscous fluid remains stationary on the boundary (no-slip boundary conditions) this is one of the oldest and most important questions in mathematical fluid mechanics, and one whose full solution does not appear likely to arrive anytime soon. I will describe some of the existing partial results concerning the vanishing viscosity limit and related problems, and will mention some potentially tractable approaches to extend some of these partial results.


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