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Title: Hölder Continuous Euler Flows with Compact Support in Time
Authors: Isett, Philip James
Advisors: Klainerman, Sergiu
Contributors: Mathematics Department
Keywords: convex integration
euler equations
fluid mechanics
onsager's conjecture
partial differential equations
Subjects: Mathematics
Issue Date: 2013
Publisher: Princeton, NJ : Princeton University
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;.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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