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Onsager's conjecture states that the conservation of energy may fail for $3D$ incompressible Euler flows with H\"{o}lder regularity below $1/3$.
The local structure of turbulence in an incompressible viscous fluid
A. N. Kolmogorov · 1941
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Statistical hydrodynamics
L. Onsager · 1949
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The multifractal spectrum of the dissipation field in turbulent flows
Charles Meneveau and Katepalli R Sreenivasan · 1987
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Joint multifractal measures: Theory and applications to turbulence
Charles Meneveau, KR Sreenivasan, P Kailasnath, and MS Fan · 1990
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From global scaling, a la kolmogorov, to local multifractal scaling in fully developed turbulence
U Frisch · 1991
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The multifractal nature of turbulent energy dissipation
Charles Meneveau and KR Sreenivasan · 1991
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Onsager’s conjecture on the energy conservation for solutions of Euler’s equation
Peter Constantin, Weinan E, and Edriss S. Titi · 1994
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Energy dissipation without viscosity in ideal hydrodynamics. I. Fourier analysis and local energy transfer
Gregory L. Eyink · 1994
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Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations
Jean Duchon and Raoul Robert · 2000
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A geometric approach to the Calderón-Zygmund estimates
Li He Wang · 2003
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Onsager and the theory of hydrodynamic turbulence
G. L. Eyink and K. R. Sreenivasan · 2006
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Energy conservation and Onsager’s conjecture for the Euler equations
A. Cheskidov, P. Constantin, S. Friedlander, and R. Shvydkoy · 2008
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The Euler equations as a differential inclusion
Camillo De Lellis and László Székelyhidi, Jr · 2009
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Loss of smoothness and energy conserving rough weak solutions for the 3 d 3d Euler equations
C. Bardos and E. Titi · 2010
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h-principle and rigidity for C 1 , α {C}^{1,\alpha} isometric embeddings. To appear in
S. Conti, C. De Lellis, and L. Székelyhidi, Jr · 2010
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Ill-posedness of the basic equations of fluid dynamics in Besov spaces
A. Cheskidov and R. Shvydkoy · 2010
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Hölder continuous Euler flows in three dimensions with compact support in time. Preprint
P. Isett · 2012
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Continuous dissipative Euler flows and a conjecture of Onsager
Camillo De Lellis and László Székelyhidi · 2013
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Dissipative continuous Euler flows
Camillo De Lellis and László Székelyhidi · 2013
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A heat flow approach to Onsager’s conjecture for the Euler equations on manifolds. To appear in
P. Isett and S.-J. Oh · 2013
2D homogeneous solutions to the Euler equation
Xue Luo and Roman Shvydkoy · 2015
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Dissipative Euler flows with Onsager-critical spatial regularity
Tristan Buckmaster, Camillo De Lellis, and László Székelyhidi, Jr · 2016
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Nonuniqueness of weak solutions to the SQG equation. Preprint
Tristan Buckmaster, Steve Shkoller, and Vlad Vicol · 2016
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Non-uniqueness and h-principle for Hölder-continuous weak solutions of the Euler equations. Preprint
S. Daneri and L. Székelyhidi, Jr · 2016
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A heat flow approach to Onsager’s conjecture for the Euler equations on manifolds
Philip Isett and Sung-Jin Oh · 2016
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On nonperiodic Euler flows with Hölder regularity
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Regularity in time along the coarse scale flow for the Euler equations. Preprint
P. Isett · 2013
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Euler equations and turbulence: analytical approach to intermittency
A. Cheskidov and R. Shvydkoy · 2014
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Dissipative Euler flows and Onsager’s conjecture
Camillo De Lellis and László Székelyhidi, Jr · 2014
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Anomalous dissipation for 1 / 5 1/5 -Hölder Euler flows
Tristan Buckmaster, Camillo De Lellis, Philip Isett, and László Székelyhidi, Jr · 2015
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A Nash-Kuiper theorem for C 1 / 5 − δ C^{1/5-\delta} immersions of surfaces in 3 3 dimensions
Camillo De Lellis, Dominik Inauen, and László Székelyhidi Jr · 2015
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On the Kinetic Energy profile of Hölder continuous Euler flows. Preprint
P. Isett and S.-J. Oh · 2015
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Philip Isett and Sung-Jin Oh · 2016
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A proof of Onsager’s conjecture. Preprint
P. Isett · 2016
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Onsager’s conjecture for admissible weak solutions. Preprint
Tristan Buckmaster, Camillo De Lellis, László Székelyhidi, Jr., and Vlad Vicol · 2017
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Hölder continuous Euler flows in three dimensions with compact support in time
Philip Isett · 2017
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Addendum: 2D homogeneous solutions to the Euler equation [ MR3359160]
Xue Luo and Roman Shvydkoy · 2017
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Onsager’s conjecture for the incompressible Euler equations in bounded domains
Claude Bardos and Edriss S. Titi · 2018
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Onsager’s conjecture and anomalous dissipation on domains with boundary
Theodore D Drivas and Huy Nguyen · 2018
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Homogeneous solutions to the 3D Euler system
Roman Shvydkoy · 2018
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