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Nonuniqueness and existence of continuous, globally dissipative Euler flows

Isett, Philip (2017) Nonuniqueness and existence of continuous, globally dissipative Euler flows. . (Submitted)

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We show that Hölder continuous, globally dissipative incompressible Euler flows (solutions obeying the local energy inequality) are nonunique and contain examples that strictly dissipate energy. The collection of such solutions emanating from a single initial data may have positive Hausdorff dimension in the energy space even if the local energy equality is imposed, and the set of initial data giving rise to such an infinite family of solutions is C^0 dense in the space of continuous, divergence free vector fields on the torus T^3.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Isett, Philip0000-0001-9038-5546
Additional Information:The work of P. Isett is supported by the National Science Foundation under Award No. DMS-1402370.
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Record Number:CaltechAUTHORS:20180626-160542363
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87364
Deposited By: Tony Diaz
Deposited On:26 Jun 2018 23:32
Last Modified:04 Aug 2022 18:43

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