On nonuniqueness of Hölder continuousglobally dissipative Euler flows

Abstract

We show that for any $\\al<\\frac 17$ there exist $\\al$-H\\"older continuous\nweak solutions of the three-dimensional incompressible Euler equation, which\nsatisfy the local energy inequality and strictly dissipate the total kinetic\nenergy. The proof relies on the convex integration scheme and the main building\nblocks of the solution are various Mikado flows with disjoint supports in space\nand time.\n