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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) http://resolver.caltech.edu/CaltechAUTHORS:20180626-160542363

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Abstract

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)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1710.11186arXivDiscussion Paper
Additional Information:The work of P. Isett is supported by the National Science Foundation under Award No. DMS-1402370.
Funders:
Funding AgencyGrant Number
NSFDMS-1402370
Record Number:CaltechAUTHORS:20180626-160542363
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180626-160542363
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87364
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:26 Jun 2018 23:32
Last Modified:26 Jun 2018 23:32

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