Hou, Thomas Y. and Shi, Zuoqiang and Wang, Shu (2011) On the Local Well-posedness of a 3D Model for Incompressible Navier-Stokes Equations with Partial Viscosity. . (Submitted) https://resolver.caltech.edu/CaltechAUTHORS:20160315-133702384
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Abstract
In this short note, we study the local well-posedness of a 3D model for incompressible Navier-Stokes equations with partial viscosity. This model was originally proposed by Hou-Lei in \cite{HouLei09a}. In a recent paper, we prove that this 3D model with partial viscosity will develop a finite time singularity for a class of initial condition using a mixed Dirichlet Robin boundary condition. The local well-posedness analysis of this initial boundary value problem is more subtle than the corresponding well-posedness analysis using a standard boundary condition because the Robin boundary condition we consider is non-dissipative. We establish the local well-posedness of this initial boundary value problem by designing a Picard iteration in a Banach space and proving the convergence of the Picard iteration by studying the well-posedness property of the heat equation with the same Dirichlet Robin boundary condition.
Item Type: | Report or Paper (Discussion Paper) | ||||||
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Record Number: | CaltechAUTHORS:20160315-133702384 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20160315-133702384 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 65367 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | Tony Diaz | ||||||
Deposited On: | 15 Mar 2016 22:54 | ||||||
Last Modified: | 03 Oct 2019 09:46 |
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