Boundary layer separation of 2-D incompressible Dirichlet flows

Quan Wang; Hong Luo; Tian Ma

doi:10.3934/dcdsb.2015.20.675

Article Contents

2015, Volume 20, Issue 2: 675-682. Doi: 10.3934/dcdsb.2015.20.675

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Boundary layer separation of 2-D incompressible Dirichlet flows

1.
Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064
2.
College of Mathematics and Software Science, Sichuan Normal University, Chengdu,Sichuan 610066

Received: February 28, 2014

Revised: May 31, 2014

Published: February 2015

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Abstract

In this paper, the solutions of Navier-Stokes equations governing 2-D incompressible flows with the Dirichlet boundary condition are analyzed. We derive a condition for boundary layer separation, and the condition is determined by initial values and external forces. More importantly, the condition can predict when and where the boundary layer separation occurs directly. In addition, we also get an algebraic equation for the separation point and the separation time. The algebraic equation can tell us where the boundary layer separation does not occur in a short period of time. The main technical tool is the geometric theory of incompressible flows developed by T. Ma and S. Wang in [15].

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Mathematics Subject Classification: Primary: 35Q30, 35Q35, 76D10, 76M99.

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References

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