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On nonuniqueness of
Hölder continuous globally dissipative Euler flows
Camillo De Lellis and Hyunju Kwon |
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Vol. 15 (2022), No. 8, 2003–2059
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Abstract |
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We show that for any there exist -Hölder continuous weak solutions of the three-dimensional incompressible Euler equation, which satisfy the local energy inequality and strictly dissipate the total kinetic energy. The proof relies on the convex integration scheme and the main building blocks of the solution are various Mikado flows with disjoint supports in space and time. |
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Keywords
Euler equations, Onsager's conjecture, the local energy
inequality, convex integration
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Mathematical Subject Classification
Primary: 35Q31
Secondary: 35D30, 76B03
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Milestones
Received: 11 September 2020
Revised: 9 February 2021
Accepted: 25 March 2021
Published: 10 February 2023
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Authors |
| Camillo De Lellis | |
| School of Mathematics Institute for Advanced Study Princeton, NJ United States |
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| Hyunju Kwon | |
| School of Mathematics Institute for Advanced Study Princeton, NJ United States |
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