@article{7a90494b8d9f44f5984f6b46acf40d1a,

title = "Nonuniqueness of weak solutions to the Navier-Stokes equation",

abstract = "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 H{\"o}lder 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.",

keywords = "Convex integration, Euler equations, Intermittency, Inviscid limit, Navier-Stokes, Turbulence, Weak solutions",

author = "Tristan Buckmaster and Vlad Vicol",

note = "Funding Information: Acknowledgments. The work of T.B. has been partially supported by the National Science Foundation grant DMS-1600868. V.V. was partially supported by the National Science Foundation grant DMS-1652134 and by an Alfred P. Sloan Research Fellowship. The authors would like to thank Maria Colombo, Camillo De Lellis, Alexandru Ionescu, Igor Kukavica, and Nader Masmoudi for their valuable suggestions and comments. Funding Information: The work of T.B. has been partially supported by the National Science Foundation grant DMS-1600868.V.V.waspartiallysup-ported by the National Science Foundation grant DMS-1652134 and by an Alfred P.Sloan Research Fellowship.The authors would like to thank Maria Colombo, Camillo De Lellis, Alexandru Ionescu, Igor Kukavica, and Nader Masmoudi for their valuable suggestions and comments Publisher Copyright: {\textcopyright} 2019 Department of Mathematics, Princet on University.",

year = "2019",

doi = "10.4007/annals.2019.189.1.3",

language = "English (US)",

volume = "189",

pages = "101--144",

journal = "Annals of Mathematics",

issn = "0003-486X",

publisher = "Princeton University Press",

number = "1",

}