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).