Hölder Continuous Euler Flows with Compact Support in Time

Abstract

Building on the recent work of C. De Lellis and L. Szekelyhidi, we construct global weak solutions to the three-dimensional incompressible Euler equations which are zero outside of a finite time interval and have velocity in the Holder class C1/5 - ε. By slightly modifying the proof, we show that every smooth solution to incompressible Euler on (-2, 2)×T3 coincides on (-1, 1)×T3 with some Holder continuous solution that is constant outside (-3/2, 3/2)×T3. We also propose a conjecture related to our main result that would imply Onsager's conjecture that there exist energy dissipating solutions to Euler whose velocity fields have Holder exponent 1/3 - ε.