Survey on time periodic problem for fluid flowunder inhomogeneous boundary condition

Hiroko Morimoto

doi:10.3934/dcdss.2012.5.631

Article Contents

2012, Volume 5, Issue 3: 631-639. Doi: 10.3934/dcdss.2012.5.631

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Survey on time periodic problem for fluid flow under inhomogeneous boundary condition

Hiroko Morimoto^1,

1.
Department of Mathematics, Meiji University, Kawasaki, 214-8571

Received: August 31, 2010

Revised: September 30, 2010

Published: May 2012

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Abstract

We consider the time dependent motion of incompressible viscous fluid with non-homogeneous boundary condition. We suppose that the bounded domain filled by the fluid has at least two boundary components, and the boundary data for the fluid velocity satisfies only the general outflow condition (GOC). The existence of solutions for the stationary problem and time periodic problem is not known in general context. We present results for the Navier-Stokes equations and the Boussinesq equations.

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Mathematics Subject Classification: Primary: 35Q30, Secondary: 76D05.

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