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On the Local Well-posedness of a 3D Model for Incompressible Navier-Stokes Equations with Partial Viscosity

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)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1107.1823arXivDiscussion Paper
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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