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This note addresses the question of energy conservation for the 2D Euler system with an $L^p$-control on vorticity.
Statistical hydrodynamics
Lars Onsager · 1949
Earlier work this paper cites.
Concentrations in regularizations for 2 2 -D incompressible flow
Ronald J. DiPerna and Andrew J. Majda · 1987
Earlier work this paper cites.
An inviscid flow with compact support in space-time
Vladimir Scheffer · 1993
Earlier work this paper cites.
Onsager’s conjecture on the energy conservation for solutions of Euler’s equation
Peter Constantin, Weinan E, and Edriss S. Titi · 1994
Earlier work this paper cites.
Energy dissipation without viscosity in ideal hydrodynamics. I. Fourier analysis and local energy transfer
Gregory L. Eyink · 1994
Earlier work this paper cites.
On the nonuniqueness of weak solution of the Euler equation
Alexander Shnirelman · 1997
Cited alongside, same era.
Inertial energy dissipation for weak solutions of incompressible Euler and Navier-Stokes equations
Jean Duchon and Raoul Robert · 2000
Cited alongside, same era.
Approximate solutions of the incompressible Euler equations with no concentrations
Milton C. Lopes Filho, Helena J. Nussenzveig Lopes, and Eitan Tadmor · 2000
Cited alongside, same era.
Energy conservation and Onsager’s conjecture for the Euler equations
Alexey Cheskidov, Peter Constantin, Susan Friedlander, and Roman Shvydkoy · 2008
Cited alongside, same era.
The Euler equations as a differential inclusion
Camillo De Lellis and László Székelyhidi, Jr · 2009
Cited alongside, same era.
Dissipative Euler flows with Onsager-critical spatial regularity
Tristan Buckmaster, Camillo De Lellis, and László Székelyhidi
Cited in the paper.
Dissipative continuous Euler flows in two and three dimensions
Antoine Choffrut, Camillo De Lellis, and László Székelyhidi
Cited in the paper.
On the energy of inviscid singular flows
Roman Shvydkoy · 2009
Later among the works it cites.
Loss of smoothness and energy conserving rough weak solutions for the 3 d 3d Euler equations
Claude Bardos and Edriss S. Titi · 2010
Later among the works it cites.
Holder continuous Euler flows with compact support in time
Philip Isett · 2013
Later among the works it cites.
Renormalized solutions of the 2D Euler equations
Gianluca Crippa and Stefano Spirito · 2015
Closest in time.
2D homogeneous solutions to the Euler equation
Xue Luo and Roman Shvydkoy · 2015
Closest in time.
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