Non-uniqueness for the Euler equations up to Onsager's critical exponent

[Ons] Onsager, L. Statistical hydrodynamics Il Nuovo Cimento (1943-1954), 6, 279–287 (1949)

1949

Earlier work this paper cites.

[Nash] Nash, J. C 1 C^{1} isometric embeddings Ann. Math. (2) 60, 3, 383–396 (1954)

1954

Earlier work this paper cites.

[CET] Constantin, P., E W. and Titi, E.S. Onsager’s conjecture on the energy conservation for solutions of Euler’s equations Comm. Math. Phys. 165, 1, 207–209 (1994)

1994

Earlier work this paper cites.

[Eyi] Eyink, G.L. Energy dissipation without viscosity in ideal hydrodynamics. I. Fourier analysis and local energy transfer Phys. D, 78, 3-4, 222–240 (1994)

1994

Earlier work this paper cites.

[DS09] De Lellis, C. and Székelyhidi Jr., L. The Euler equations as a differential inclusion Ann. Math. (2), 170, 3, 1417–1436 (2009)

2009

Earlier work this paper cites.

[DS10] De Lellis, C. and Székelyhidi Jr., L. On admissibility criteria for weak solutions of the Euler equations Arch. Rat. Mech. Anal. 195, 1, 225–260 (2010)

2010

Earlier work this paper cites.

[BDS] Brenier, Y., De Lellis, C. and Székelyhidi Jr., L. Weak-strong uniqueness for measure-valued solutions Comm. Math. Phys. 305, 351–361 (2011)

2011

Earlier work this paper cites.

[CDSz] Conti, S., De Lellis, C. and Székelyhidi Jr, L. h h -principle and rigidity for C 1 , α C^{1,\alpha} isometric embeddings Nonlinear Partial Differential Equations: The Abel Symposium 2010, 83–116 (2012)

2012

Earlier work this paper cites.

[DS12] De Lellis, C. and Székelyhidi Jr., L. The h h -principle and the equations of fluid dynamics Bull. Amer. Math. Soc. 49, 3, 347–375 (2012)

2012

Cited alongside, same era.

[SzW] Székelyhidi Jr., L. and Wiedemann, E. Young measures generated by ideal incompressible fluid flows Arch. Rat. Mech. Anal. 206, 1, 333–366 (2012)

2012

Cited alongside, same era.

[DS13] De Lellis, C. and Székelyhidi Jr., L. Dissipative continuous Euler flows Invent. Math. 193, 2, 377–407 (2013)

2013

Cited alongside, same era.

[Dan] Daneri, S. Cauchy problem for dissipative Hölder solutions to the incompressible Euler equations Comm. Math. Phys. 329, 2, 745–786 (2014)

2014

Cited alongside, same era.

[DS14] De Lellis, C. and Székelyhidi Jr., L. Dissipative Euler flows and Onsager’s conjecture J. Eur. Math. Soc. 16, 7, 1467–1505 (2014)

2014

Cited alongside, same era.

[IO] Isett, P. and Oh, S.-J. On the kinetic energy profile of Hölder continuous Euler flows Ann. Inst. H. Poincaré Anal. Non Linéaire, pp. 1–20 (2016)

2016

Later among the works it cites.

[DanSz] Daneri, S. and Székelyhidi Jr., L. Non-uniqueness and h h -principle for Hölder-continuous weak solutions of the Euler equations Arch. Rat. Mech. Anal. 224, 471–514 (2017)

2017

Later among the works it cites.

[DS17] De Lellis, C. and Székelyhidi Jr., L. High dimensionality and h-principle in PDE Bull. Amer. Math. Soc. (N.S.), vol. 54, no. 2, pp. 247–282 (2017)

2017

Later among the works it cites.

[BDSV] Buckmaster, T., De Lellis, C., Székelyhidi Jr., L. and Vicol, V. Onsager’s conjecture for admissible weak solutions Comm. Pure Appl. Math. 72, 2, 229–274 (2018)

2018

Later among the works it cites.

[CDD] Colombo, M.; De Lellis, C.; De Rosa, L. Ill-posedness of Leray solutions for the ipodissipative Navier?Stokes equations Comm. Math. Phys. 362 no. 2, 659–688 (2018)