Jian-Guo Liu, University of Maryland

A new approach for analysis and computation of Navier-Stokes Equation in bounded domains

Friday December 1st, 4pm, Phillips 383
(refreshments served in Phillips 330 starting at 3:30)

Abstract: In this talk, I review the recent exciting development in consistent projection methods for incompressible Navier-Stokes Equation (NSE) first. I will then focus on a new approach based upon a new, sharp estimate for the commutator of the Laplacian and Helmholtz projection operators, which shows that NSE can be regarded as a perturbed diffusion equation, rather than a perturbed Stokes system. This leads to stability results for discretization schemes that provide simple proofs of the existence and uniqueness of local strong solutions for NSE. Our findings help explain the success of recently developed numerical methods that are fast, accurate near boundaries, and simple and flexible in structure. This is a joint work with Bob Pego (CMU) and Jie Liu (UC-Irvine).