open access

https://doi.org/10.14943/84221

https://hdl.handle.net/2115/69881

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

英語

well-chosen weak solutions, Serrin’s uniquenes theorem

2015-10-27

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

1077

1-10

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.

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