Thursday, March 1, 2006

Speaker: Jeffrey Humpherys, Brigham Young University
Stability of viscous shocks in isentropic gas dynamics
One of the key problems in conservation laws is the stability problem for viscous traveling waves. While there has been a great deal of work for small-amplitude fronts, little is currently known about the stability of large-amplitude fronts. In this talk, we examine the stability problem for viscous shocks for the one-dimensional isentropic compressible Navier-Stokes equations, also known as the p-system with real viscosity. We show that large-amplitude shocks are stable using a combination of energy estimates and numerical Evans function computation.

Thursday, February 1, 2006

Speaker: Florentina Tone, University of West Florida
Long-time Stability of the Implicit Euler Scheme for the 2d Navier-Stokes Equations
In this talk I will discuss the H^1-stability for all positive time of the fully implicit Euler scheme for the 2D Navier-Stokes equations. More precisely, I will discretize the Navier-Stokes equations in time using the implicit Euler scheme and with the aid of a discrete Gronwall lemma and of a discrete uniform Gronwall lemma, I will prove that the numerical scheme is unconditionally stable (uniformly in time).