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math.AP2025
Dissipative solutions for 2D Onsager's conjecture
Lili Du, Xinliang Li, Weikui Ye
In 1949, L. Onsager conjectured that weak solutions of the Euler equations in are energy conservative when , whereas nonconservative solutions exist when…
math.AP2025
On Onsager-type conjecture for the Elsässer energies of the ideal MHD equations
Changxing Miao, Yao Nie, Weikui Ye
In this paper, we investigate the ideal magnetohydrodynamics (MHD) equations on tours $\TTT^d$. For , we resolve the flexible part of Onsager-type conjecture for Elsässer ener…