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

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

No reviews yet.

No comments yet.