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 C<super>1/5 - &epsilon;</super>.

By slightly modifying the proof, we show that every smooth solution to incompressible Euler on (-2, 2)&times;T<super>3</super> coincides on (-1, 1)&times;T<super>3</super> with some Holder

continuous solution that is constant outside (-3/2, 3/2)&times;T<super>3</super>. 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 - &epsilon;.