Initial values for the Navier-Stokes equations in spaces with weights in time

Farwig, Reinhard; GIGA, YOSHIKAZU; Hsu, Pen-Yuan

Hokkaido University Preprint Series in Mathematics, 2014, 1060, 1-16

Permalink : https://doi.org/10.14943/84204

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DOI	https://doi.org/10.14943/84204
URI	https://hdl.handle.net/2115/69864
タイトル	Initial values for the Navier-Stokes equations in spaces with weights in time
著者	Farwig, Reinhard ; GIGA, YOSHIKAZU ; Hsu, Pen-Yuan
著者名 Farwig, Reinhard
著者名 GIGA, YOSHIKAZU
著者名 Hsu, Pen-Yuan
言語	英語
キーワード	Instationary Navier-Stokes system
	initial values
	local strong solutions
	weighted Serrin condition
	well-chosen weak solutions
	restricted Serrin's uniquenesss theorem
発行日	2014-08-25
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	1060
ページ	1-16
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record