2022-05-18T22:31:40Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/697982018-04-25T23:44:11Zhdl_2115_45007hdl_2115_116Solution formula for the vorticity equations in the half plane with application to high vorticity creation at zero viscosity limitMaekawa, YasunoriNavier-Stokes equationsVorticity equationsNo-slip boundary conditionsInviscid limit410We consider the Navier-Stokes equations for viscous incompressible flows in the half plane under the no-slip boundary condition. In this paper we first establish a solution formula for the vorticity equations through the appropriate vorticity formulation. The formula is then applied to establish the asymptotic expansion of vorticity fields at ! 0 that holds at least up to the time c 1=3, where is the viscosity coefficient and c is a constant. As a consequence, we get a natural sufficient condition on the initial data for the vorticity to blow up in the inviscid limit, together with explicit estimates.Departmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69798info:doi/10.14943/84139https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69798/1/pre992.pdfHokkaido University Preprint Series in Mathematics9921292011-12-26engpublisher