Mathematical issues in stability of viscoelastic flows<br/><br/><br/><br/>

Wednesday, October 14, 2009 - 9:00am - 9:40am
EE/CS 3-180
Michael Renardy (Virginia Polytechnic Institute and State University)
Traditional hydrodynamic stability studies infer stability of a flow from
a computation of eigenvalues of the linearized system. While this is well
justified for the Navier-Stokes equations, no rigorous result along these lines
is known for general systems of partial differential equations; indeed there are
counterexamples for lower order perturbations of the wave equations. This lecture
will discuss how recent results on advective equations can be applied to creeping
flows of viscoelastic fluids of Maxwell or Oldroyd type. For spatially periodic
flows, stability can be reduced to the study of a) the eigenvalues, and b) a system
of non-autonomous ordinary differential equations that arises from a geometric
optics approximation for short waves. A more complete result for the upper convected
Maxwell model will also be discussed.
MSC Code: