Cauchy problem for dissipative Hölder solutions to the incompressible Euler equations

Abstract

We consider solutions to the Cauchy problem for the incompressible Euler equations on the 3-dimensional torus which are continuous or Hölder 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 (Hölder) continuous initial vector fields starting from which there exist infinitely many (Hölder) continuous solutions with preassigned total kinetic energy.

References in corpus (1)

• Dissipative continuous Euler flows in two and three dimensions