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This paper addresses the problem of energy conservation for the two- and three-dimensional density-dependent Euler equations.
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C. De Lellis, and L. Székelyhidi, Jr., Dissipative Euler flows and OnsagerÕs conjecture. J. Eur. Math. Soc. (JEMS) 16
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A. Cheskidov, P. Constantin, S. Friedlander, and R. Shvydkoy, Energy conservation and Onsagers conjecture for the Euler equations. Nonlinearity 21
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C. De Lellis, and L. Székelyhidi, Jr., The Euler equations as a differential inclusion. Ann. of Math. 170
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L. C. Evans, Partial differential equations . Second edition, Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 2010
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C. De Lellis, and L. Székelyhidi, Jr., Continuous dissipative Euler flows and a conjecture of Onsager. European Congress of Mathematics, Eur. Math. Soc., Zürich (2013), 13-29
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C. De Lellis, and L. Székelyhidi, Jr., Dissipative continuous Euler flows. Invent. Math. 193
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C.Yu, Energy conservation for the weak solutions of the compressible Navier-Stokes equations. to appear in Arch. Ration. Mech. Anal
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A. Vasseur, C. Yu, Existence of global weak solutions for 3D degenerate compressible Navier-Stokes equations. Invent. Math. 206 (2016), no. 3, 935-974
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2017
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E. Feireisl, P. Gwiazda, A. Swierczewska-Gwiazda, and E. Wiedemann, Regularity and energy conservation for the compressible Euler equations. Arch. Ration. Mech. Anal. 223
2017
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