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On the continuity of the solutions to the Navier-Stokes equations with initial data in critical Besov spaces
| Title: | On the continuity of the solutions to the Navier-Stokes equations with initial data in critical Besov spaces |
| Authors: | Farwig, Reinhard Browse this author | | GIGA, YOSHIKAZU Browse this author | | Hsu, Pen-Yuan Browse this author |
| Keywords: | Instationary Navier-Stokes system | | initial values | | weighted Serrin condition | | limiting type of Besov space | | continuity of solutions | | stability of solutions |
| Issue Date: | 14-Jul-2016 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1093 |
| Start Page: | 1 |
| End Page: | 17 |
| Abstract: | It is well-known that there exists a unique local-in-time strong solution u of the initial-boundary value problem for the Navier-Stokes sytem in a three-dimensional smooth bounded domain when the initial velocity u0 belongs to critical Besov spaces. A typical space is B = B1+3=q q;s with 3 < q < 1, 2 < s < 1 satisfying 2=s+3=q 1 or B = B 1+3=q q;1 . In this paper we show that the solution u is continuous in time up to initial time with values in B. Moreover, the solution map u0 7! u is locally Lip- schitz from B to C ([0; T];B). This implies that in the range 3 < q < 1, 2 < s 1 with 3=q + 2=s 1 the problem is well-posed which is in strong contrast to norm in ation phenomena for B1 1;s, 1 s < 1. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69897 |
| 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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