Speaker: Bob Pego
Title: Incompressible Navier-Stokes dynamics in bounded domains---a
new approach for analysis and computation
Abstract: Based upon a new, sharp estimate for the commutator of the Laplacian
and Helmholtz projection operators, we show that the pressure gradient
is bounded in L2 norm by the viscosity term times a constant less than
one, up to lower order terms. By consequence, NSE can be regarded as
a perturbed diffusion equation, rather than a perturbed Stokes system.
This leads to stability results for discretization schemes that
(a) provide simple proofs of existence and uniqueness of local strong
solutions, and (b) help explain the success of recently developed
numerical methods that are fast, accurate near boundaries, and simple
and flexible in structure. This is joint work with Jian-Guo Liu and
Jie Liu (Maryland).
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