| Speaker: | Jean-Luc Guermond, Texas A&M University |
| Title: | New results on the characterization of suitable weak solutions to the 3D Navier--Stokes equations in bounded domains with Dirichlet boundary conditions |
| Time: | 3:00-4:00 pm |
| Place: | Blocker 628 |
Faedo-Galerkin weak solutions to the Navier--Stokes equations supplemented with Dirichlet boundary conditions in bounded domains are suitable in the sense of V. Sheffer provided they are constructed using finite-dimensional approximation spaces having a discrete commutator property and satisfying a proper inf-sup condition. Low order mixed finite element spaces appear to be acceptable for this purpose. This results extend an earlier result of the author that holds in the three-dimensional torus only. The main technical difference is that pressure estimates are more involved and are derived by using negative exponents of the Stokes operator in order to derive bounds similar to those of Sohr and Von Wahl. This result reduces the gap between the class of weak solutions and that of the suitable weak solutions.
Last revised: 09/28/06 By: christov@math