On Non-uniqueness of H\"{o}lder continuous globally dissipative Euler flows
Analysis of PDEs
2023-02-15 v2
Abstract
We show that for any there exist -H\"older continuous weak solutions of the three-dimensional incompressible Euler equation, which satisfy the local energy inequality and strictly dissipate the total kinetic energy. The proof relies on the convex integration scheme and the main building blocks of the solution are various Mikado flows with disjoint supports in space and time.
Keywords
Cite
@article{arxiv.2006.06482,
title = {On Non-uniqueness of H\"{o}lder continuous globally dissipative Euler flows},
author = {Camillo De Lellis and Hyunju Kwon},
journal= {arXiv preprint arXiv:2006.06482},
year = {2023}
}
Comments
v2: a minor issue on the well-definedness of the mollification along the flow is fixed