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Hokkaido University Preprint Series in Mathematics >
Initial values for the Navier-Stokes equations in spaces with weights in time
| Title: | Initial values for the Navier-Stokes equations in spaces with weights in time |
| Authors: | Farwig, Reinhard Browse this author | | GIGA, YOSHIKAZU Browse this author | | Hsu, Pen-Yuan Browse this author |
| Keywords: | Instationary Navier-Stokes system | | initial values | | local strong solutions | | weighted Serrin condition | | well-chosen weak solutions | | restricted Serrin's uniquenesss theorem |
| Issue Date: | 25-Aug-2014 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1060 |
| Start Page: | 1 |
| End Page: | 16 |
| Abstract: | We consider the nonstationary Navier-Stokes system in a smooth bounded domain R3 with initial value u0 2 L2 ( ). It is an important question to determine the optimal initial value condition in order to prove the existence of a unique local strong solution satisfying Serrin's condition. In this paper, we introduce a weighted Serrin condition that yields a necessary and su cient initial value condition to guarantee the existence of R local strong solutions u( ) contained in the weighted Serrin class T 0 ( ku( )kq)s d < 1 with 2 s + 3 q = 1 2 , 0 < < 1 2 . Moreover, we prove a restricted weak-strong uniqueness theorem in this Serrin class. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69864 |
| 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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