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arXiv · 2204.03344

Infinitely many non-conservative solutions for the three-dimensional Euler equations with arbitrary initial data in $C^{1/3-\epsilon}$

Calvin Khor·Changxing Miao·Weikui Ye
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Abstract

Let $0<\beta<\bar\beta<1/3$. We construct infinitely many distributional solutions in $C^{\beta}_{x,t}$ to the three-dimensional Euler equations that do not conserve the energy, for a given initial data in $C^{\bar\beta}$. We also show that there is some limited control on the increase in the energy for $t>1$.

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Calvin Khor, Changxing Miao, Weikui Ye. 2022-04-07. Infinitely many non-conservative solutions for the three-dimensional Euler equations with arbitrary initial data in $C^{1/3-\epsilon}$. https://arxiv.org/abs/2204.03344

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