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On the continuity of the solutions to the Navier-Stokes equations with initial data in critical Besov spaces

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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
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 = B􀀀1+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 B􀀀1 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

Submitter: 数学紀要登録作業用

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