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The Navier-Stokes equations with initial values in Besov spaces of type $B_{q,\infty}^{-1+3/q}$
| Title: | The Navier-Stokes equations with initial values in Besov spaces of type $B_{q,\infty}^{-1+3/q}$ |
| 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 | | limiting type of Besov space | | restricted Serrin's uniqueness theorem |
| Issue Date: | 20-Jun-2016 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1092 |
| Start Page: | 1 |
| End Page: | 21 |
| Abstract: | We consider weak solutions of the instationary Navier-Stokes system in a smooth bounded domain R3 with initial value u0 2 L2 ( ). It is known that a weak solution is a local strong solution in the sense of Serrin if u0 satis es the optimal initial value condition u0 2 B1+3=q q;sq with Serrin exponents sq > 2; q > 3 such that 2 sq + 3 q = 1. This result has recently been generalized by the authors to Rweighted Serrin conditions such that u is contained in the weighted Serrin class T 0 ( ku( )kq)s d < 1 with 2 s + 3 q = 1 2 , 0 < < 1 2 . This regularity is guaranteed if and only if u0 is contained in the Besov space B1+3=q q;s . In this article we consider the limit case of initial values in the Besov space B1+3=q q;1 and in its subspace B 1+3=q q;1 based on the continuous interpolation functor. Special emphasis is put on questions of uniqueness within the class of weak solutions. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69896 |
| 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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