2024-03-29T02:39:48Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/697952022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116A remark on a Liouville problem with boundary for the Stokes and the Navier-Stokes equationsGIGA, YOSHIKAZUopen accessLiouville problemNavier-Stokes equationsnon-slip boundary conditionPoiseuille type flow410We construct a Poiseuille type ow 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.Department of Mathematics, Hokkaido University2011-11-18engdepartmental bulletin paperVoRhttps://doi.org/10.14943/84136http://hdl.handle.net/2115/6979510.14943/84136Hokkaido University Preprint Series in Mathematics989116https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69795/1/pre989.pdfapplication/pdf163.12 KB2011-11-18