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Solution formula for the vorticity equations in the half plane with application to high vorticity creation at zero viscosity limit
| Title: | Solution formula for the vorticity equations in the half plane with application to high vorticity creation at zero viscosity limit |
| Authors: | Maekawa, Yasunori Browse this author |
| Keywords: | Navier-Stokes equations | | Vorticity equations | | No-slip boundary conditions | | Inviscid limit |
| Issue Date: | 26-Dec-2011 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 992 |
| Start Page: | 1 |
| End Page: | 29 |
| Abstract: | We 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. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69798 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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