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Hokkaido University Preprint Series in Mathematics >
Global existence of two-dimensional Navier-Stokes flow with nondecaying initial velocity
| Title: | Global existence of two-dimensional Navier-Stokes flow with nondecaying initial velocity |
| Authors: | Giga, Y. Browse this author | | Matsui, S. Browse this author | | Sawada, O. Browse this author |
| Keywords: | nondecaying initial velocity | | two-dimentional Navier-Stokes flow | | global existence | | logarithmic Gronwall inequality | | vorticity equation. |
| Issue Date: | 1-Nov-2000 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 503 |
| Start Page: | 1 |
| End Page: | 19 |
| Abstract: | A global-in-time unique smooth solution is constructed for the Cauchy problem of the Navier-Stokes equations in the plane when initial velocity field is merely bouncled not necessary square-integrable. The proof is based on a uniform bound for the vorticity which is only valid for planar flows. The uniform bound for the vorticity yields a coarse globally-intime a priori estimate for the maximum norm of the velocity which is enough to extend a local solution. A global existence of solution for a q-th integrable initial velocity field is also established when q > 2. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69253 |
| 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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