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A remark on a Liouville problem with boundary for the Stokes and the Navier-Stokes equations

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  • We construct a Poiseuille type flow which is a bounded entire solution of the nonstationary Navier-Stokes and the Stokes equations in a half space with non-slip boundary condition. Our result in particular implies that there is a nontrivial solution for the Liouville problem under the non-slip boundary condition. A review for cases of the whole space and a slip boundary condition is included.
    Mathematics Subject Classification: Primary: 35Q30; Secondary: 35B53, 76D05.


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