Non-conservation of a generalized helicity in the Euler equations

Vikram Giri, Hyunju Kwon, Matthew Novack

For a $C_{t,x}^1$ solution $u$ to the incompressible 3D Euler equations, the helicity $H(u(t))={\int }_{{\mathbb{T}}^3}u\cdot \text{curl}u$ is constant in time. For general low-r…