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We give a simple proof of Onsager's conjecture concerning energy conservation for weak solutions to the Euler equations on any compact Riemannian manifold, extending the results of Constantin-E-Titi and Cheskidov-Constantin-Friedlander-Shvydkoy in the flat case.
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A. Cheskidov, P. Constantin, S. Friedlander, and R. Shvydkoy, Energy conservation and Onsager’s conjecture for the Euler equations , Nonlinearity 21
Dissipative continuous Euler flows in two and three dimensions. Preprint
A. Choffrut, C. De Lellis, and L. Székelyhidi, Jr · 2012
Later among the works it cites.
by same author, Dissipative continuous Euler flows , arXiv.org (2012)
2012
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by same author, Dissipative Euler Flows and Onsager’s Conjecture , arXiv.org (2012)
2012
Later among the works it cites.
P. Isett, Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time , arXiv.org (2012)
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T. Buckmaster, Onsager’s conjecture almost everywhere in time , arXiv.org (2013)
2013
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T. Buckmaster, C. De Lellis, and L. Székelyhidi, Jr, Transporting microstructure and dissipative Euler flows , arXiv.org (2013)
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2008
Cited alongside, same era.
C. De Lellis and L. Székelyhidi, Jr, The Euler equations as a differential inclusion , Annals of Mathematics (2009)
2009
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R. Shvydkoy, Lectures on the Onsager conjecture , Discrete Contin. Dyn. Syst. Ser. S 3
2010
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2013
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h-Principles for the Incompressible Euler Equations
A. Choffrut · 2013
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