A proof of Onsager's conjecture (Q1621947)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A proof of Onsager's conjecture |
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A proof of Onsager's conjecture (English)
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12 November 2018
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The author of this works presents his proof for Onsager's conjecture, negative direction, which states that when the speed of incompressible liquid \(v \in C_tC_x^\alpha\) instead of \(v\in C^1\), then for every \(\alpha<1/3\) there exist periodic weak solutions of the 3D Euler equation such that the conservation of energy fails. It is shown here that there is a non-zero solution such that \(v\) is identically zero outside a finite time interval that fails to conserve energy for any \(a<1/3\).
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Euler equations
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incompressible
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weak solutions
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energy conservation
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energy dissipation
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regularity
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anomalous dissipation
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turbulence
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fluid dynamics
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convex integration
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nonuniqueness
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