2016年8月
Navier-Stokes flow in the weighted Hardy space with applications to time decay problem
JOURNAL OF DIFFERENTIAL EQUATIONS
- ,
- 巻
- 261
- 号
- 3
- 開始ページ
- 1712
- 終了ページ
- 1755
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1016/j.jde.2016.04.014
- 出版者・発行元
- ACADEMIC PRESS INC ELSEVIER SCIENCE
The asymptotic expansions of the Navier-Stokes flow in R-n and the rates of decay are studied with aid of weighted Hardy spaces. Fujigaki and Miyakawa [12], Miyakawa [28] proved the nth order asymptotic expansion of the Navier-Stokes flow if initial data decays like (1 + vertical bar x vertical bar)(-n-1) and if nth moment of initial data is finite. In the present paper, it is clarified that the moment condition for initial data is essential in order to obtain higher order asymptotic expansion of the flow and to consider the rapid time decay problem. The second author [39] established the weighted estimates of the strong solutions in the weighted Hardy spaces with small initial data which belongs to L-n and a weighed Hardy space. Firstly, the refinement of the previous work [39] is achieved with alternative proof. Then the existence time of the solution in the weighted Hardy spaces is characterized without any Hardy norm. As a result, in two dimensional case the smallness condition on initial data is completely removed. As an application, the rapid time decay of the flow is investigated with aid of asymptotic expansions and of the symmetry conditions introduced by Brandolese [3]. (C) 2016 Elsevier Inc. All rights reserved.
- リンク情報
- ID情報
-
- DOI : 10.1016/j.jde.2016.04.014
- ISSN : 0022-0396
- eISSN : 1090-2732
- Web of Science ID : WOS:000376835700003