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On Masuda uniqueness theorem for Leray–Hopf weak solutions in mixed-norm spaces

Authors :
Timothy Robertson
Tuoc Phan
Source :
European Journal of Mechanics - B/Fluids. 90:18-28
Publication Year :
2021
Publisher :
Elsevier BV, 2021.

Abstract

We revisit the well-known work of K. Masuda in 1984 on the weak–strong uniqueness of L ∞ L 3 Leray–Hopf weak solutions of Navier–Stokes equation. We modify the argument, and extend the uniqueness result to the scaling critical anisotropic Lebesgue space with mixed-norms. As a consequence, our results cover the class of initial data and solutions which may be singular or decay with different rates along different spatial variables. The result relies on the establishment of several refined properties of solutions of the Stokes and Navier–Stokes equations in mixed-norm Lebesgue spaces which seem to be of independent interest.

Details

ISSN :
09977546
Volume :
90
Database :
OpenAIRE
Journal :
European Journal of Mechanics - B/Fluids
Accession number :
edsair.doi...........1f36dedf679ad1b2411b5c6e46bbbd64
Full Text :
https://doi.org/10.1016/j.euromechflu.2021.08.001