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Well-chosen Weak Solutions of the Instationary Navier-Stokes System and Their Uniqueness

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Title: Well-chosen Weak Solutions of the Instationary Navier-Stokes System and Their Uniqueness
Authors: Farwig, Reinhard Browse this author
GIGA, YOSHIKAZU Browse this author
Keywords: Navier-Stokes equations
initial values
strong Ls (Lq)-solutions
well-chosen weak solutions, Serrin’s uniquenes theorem
Issue Date: 27-Oct-2015
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 1077
Start Page: 1
End Page: 10
Abstract: We clarify the notion of well-chosen weak solutions of the instationary Navier-Stokes system recently introduced by the authors and P.-Y. Hsu in the article Initial values for the Navier-Stokes equations in spaces with weights in time, Funkcialaj Ekvacioj (2015). Well-chosen weak solutions have initial values in L2 ( ) contained also in a quasi-optimal space of Besov type of initial values such that nevertheless Serrin’s Uniqueness Theorem cannot be applied. However, we find universal conditions such that a weak solution given by a concrete approximation method coincides with the strong solution in a weighted function class of Serrin type.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69881
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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