Calculus of Variations and Geometric Measure Theory

S. Daneri

Cauchy problem for dissipative Hölder solutions to the incompressible Euler equations

created by daneri on 04 Dec 2020


Published Paper

Inserted: 4 dec 2020

Journal: Comm. Math. Phys.
Year: 2014

ArXiv: 1302.0988 PDF


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