*Published Paper*

**Inserted:** 4 dec 2020

**Journal:** Comm. Math. Phys.

**Year:** 2014

**Abstract:**

We consider solutions to the Cauchy problem for the incompressible Euler equations on the 3-dimensional torus which are continuous or H\"older continuous for any exponent $\theta<1/16$. Using the convex integration techniques introduced in \cite{De Lellis-Szekelyhidi 2012}, we prove the existence of infinitely many (Hölder) continuous initial vector fields starting from which there exist infinitely many (H\"older) continuous solutions with preassigned total kinetic energy