Weakly Nonlinear-Dissipative Approximations of Hyperbolic-Parabolic Systems with Entropy

Computational and Applied Mathematics Colloquium

Meeting Details

For more information about this meeting, contact Hope Shaffer, Jinchao Xu, Kris Jenssen.

Speaker: David Levermore, University of Maryland

Abstract: Hyperbolic-parabolic systems have spatially homogeneous stationary solutions. When the dissipation is weak, one can derive weakly nonlinear-dissipative approximations that govern perturbations of these solutions. These approximations are quadratically nonlinear. Up to a linear transformation, they are independent of the dependent variables used to express the original system. When the original system has an entropy, the approximation is formally dissipative in a natural Hilbert space. We show that under a mild structural hypothesis, this approximation has global weak solutions for all initial data in that Hilbert space. This theory applies to the compressible Navier-Stokes system. The resulting approximate system is an incompressible Navier-Stokes system coupled to equations that govern the acoustic modes. The solution of this approximate system is unique if the incompressible modes are uniquely determined.

Room Reservation Information

Room Number: 106 McAllister

Date: 04/04/2008

Time: 3:35pm - 4:25pm