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June 2018 Well-chosen weak solutions of the instationary Navier-Stokes system and their uniqueness
Reinhard FARWIG, Yoshikazu GIGA
Hokkaido Math. J. 47(2): 373-385 (June 2018). DOI: 10.14492/hokmj/1529308824

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 {\em Initial values for the Navier-Stokes equations in spaces with weights in time, Funkcialaj Ekvacioj} (2016). Well-chosen weak solutions have initial values in $L^{2}_{\sigma}(\Omega)$ contained also in a quasi-optimal scaling-invariant space of Besov type 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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Reinhard FARWIG. Yoshikazu GIGA. "Well-chosen weak solutions of the instationary Navier-Stokes system and their uniqueness." Hokkaido Math. J. 47 (2) 373 - 385, June 2018. https://doi.org/10.14492/hokmj/1529308824

Information

Published: June 2018
First available in Project Euclid: 18 June 2018

zbMATH: 06901711
MathSciNet: MR3815298
Digital Object Identifier: 10.14492/hokmj/1529308824

Subjects:
Primary: 35B65, 35Q30, 76D03, 76D05

Rights: Copyright © 2018 Hokkaido University, Department of Mathematics

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Vol.47 • No. 2 • June 2018
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