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

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84204

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
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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