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On vorticity directions near singularities for the Navier-Stokes ows with infinite energy
| Title: | On vorticity directions near singularities for the Navier-Stokes ows with infinite energy |
| Authors: | Giga, Yoshikazu Browse this author | | Miura, Hideyuki Browse this author |
| Issue Date: | 12-Apr-2010 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 956 |
| Start Page: | 1 |
| End Page: | 18 |
| Abstract: | We give a geometric nonblow up criterion on the direction of the vorticity for the three dimensional Navier-Stokes flow whose initial data is just bounded and may have infinite energy. We prove that under a restriction on behavior in time (type I condition) the solution does not blow up if the vorticity direction is uniformly continuous at place where vorticity is large. This improves the Lipschitz regularity condition for the vorticity direction first introduced by P. Constantin and C. Fefferman (1993) for finite energy (weak) solution. Our method is based on a simple blow up argument which says that the situation looks like two-dimensional under continuity of the vorticity direction. We also discuss about boundary value problems. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69763 |
| 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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