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For initial datum of finite kinetic energy, Leray has proven in 1934 that there exists at least one global in time finite energy weak solution of the 3D Navier-Stokes equations. In this paper we prove that weak solutions of the 3D Navier-Stokes equations are not unique in the class of weak solutions with finite kinetic energy. Moreover, we prove that Hölder continuous dissipative weak solutions of the 3D Euler equations may be obtained as a strong vanishing viscosity limit of a sequence of finite energy weak solutions of the 3D Navier-Stokes equations.
@article{10_4007_annals_2019_189_1_3,
author = {Tristan Buckmaster and Vlad Vicol},
title = {Nonuniqueness of weak solutions to the {Navier-Stokes} equation},
journal = {Annals of mathematics},
pages = {101--144},
publisher = {mathdoc},
volume = {189},
number = {1},
year = {2019},
doi = {10.4007/annals.2019.189.1.3},
mrnumber = {3898708},
zbl = {07003146},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.1.3/}
}
TY - JOUR AU - Tristan Buckmaster AU - Vlad Vicol TI - Nonuniqueness of weak solutions to the Navier-Stokes equation JO - Annals of mathematics PY - 2019 SP - 101 EP - 144 VL - 189 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.1.3/ DO - 10.4007/annals.2019.189.1.3 LA - en ID - 10_4007_annals_2019_189_1_3 ER -
%0 Journal Article %A Tristan Buckmaster %A Vlad Vicol %T Nonuniqueness of weak solutions to the Navier-Stokes equation %J Annals of mathematics %D 2019 %P 101-144 %V 189 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2019.189.1.3/ %R 10.4007/annals.2019.189.1.3 %G en %F 10_4007_annals_2019_189_1_3
Tristan Buckmaster; Vlad Vicol. Nonuniqueness of weak solutions to the Navier-Stokes equation. Annals of mathematics, Tome 189 (2019) no. 1, pp. 101-144. doi: 10.4007/annals.2019.189.1.3
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