Calculus of Variations and Geometric Measure Theory

C. De Lellis - H. Kwon

On Non-uniqueness of Hoelder continuous globally dissipative Euler flows

created by delellis on 01 Dec 2020
modified on 03 Aug 2021


Accepted Paper

Inserted: 1 dec 2020
Last Updated: 3 aug 2021

Journal: To appear in Analysis and PDEs
Year: 2020


We show that for any $\alpha<\frac{1}{7}$ there exist $\alpha$-Hölder 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.