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

arxiv: 2204.03344 · v1 · pith:4VTTDURPnew · submitted 2022-04-07 · 🧮 math.AP

Infinitely many non-conservative solutions for the three-dimensional Euler equations with arbitrary initial data in C^(1/3-ε)

Calvin Khor , Changxing Miao , Weikui Ye This is my paper

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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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