We show that for any alpha < 1/7 there exist alpha-Holder 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.
On nonuniqueness of Hölder continuous globally dissipative Euler flows
De Lellis, C.;
2022-01-01
Abstract
We show that for any alpha < 1/7 there exist alpha-Holder 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.File in questo prodotto:
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