Analytical and Computational Challenges of Incompressible Flows at High Reynolds Number

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Pressure Estimate for the Incompressible Navier-Stokes Equation in a Bounded Domain

Jian-Guo Liu

                                Institute for Physical Science and Technology, University of Maryland

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 Bob Pego (CMU) and Jie Liu (Maryland).
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