PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Stephanie Zerby, Joseph Roberts, Yuxi Zheng.

Title:Some ill-posed problems in free-surface fluid dynamics
Seminar:Hyperbolic and Mixed Type PDEs Seminar
Speaker:David Ambrose, Drexel University
Abstract:
Certain problems in free-surface fluid dynamics are famously known to have ill-posed initial value problems. For the unregularized vortex sheet and for certain Boussinesq equations, the ill-posedness is suggested by linear theory. We will discuss proofs that the full systems have ill-posed initial value problems. For the vortex sheet, we will discuss older work of Duchon and Robert or Caflisch and Orellana, and we will see how the Duchon-Robert approach can be adapted to the Boussinesq case. Ill-posedness can also arise for certain problems more subtly, and we will discuss the ill-posedness of the initial value problem for truncated series models of water waves; this is related to the numerical method of Craig and Sulem for water waves. The truncated series models are linearly well-posed, and the full water wave equations are also well-posed, but we will present evidence (and discuss progress towards a proof) that these model equations are not well-posed.

Room Reservation Information

Room Number:MB216
Date:01 / 21 / 2016
Time:10:00am - 11:00am