Cauchy problem for dissipative H\"older solutions to the incompressible Euler equations

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 $\theta<\frac{1}{16}$. Using the techniques introduced in \cite{DS12} and \cite{DS12H}, we prove the existence of infinitely many (H\"older) continuous initial vector fields starting from which there exist infinitely many (H\"older) continuous solutions with preassigned total kinetic energy.