# American Institute of Mathematical Sciences

June  2012, 5(3): 631-639. doi: 10.3934/dcdss.2012.5.631

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

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

Received  September 2010 Revised  October 2010 Published  October 2011

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.
Citation: Hiroko Morimoto. Survey on time periodic problem for fluid flow under inhomogeneous boundary condition. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 631-639. doi: 10.3934/dcdss.2012.5.631
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