Dissipative continuous Euler flows

By Camillo De Lellis, L. Sz'ekelyhidi. 2012

426 citations recorded by the source corpus.

We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/eb58810fe533f6c9f9647fc0147d326e7bce45d3

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Wild solutions of the Navier–Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1 (2018, background): “[10], culminating in the eventual resolution of Onsager’s conjecture by Isett [19] (cf.”
Anomalous dissipation for 1/5-Hölder Euler flows (2015, methodology): “will be based on the constructions given in [11, 9].”
Convex integration and phenomenologies in turbulence (2019, methodology): “The work [48], has since been extended and adapted by various authors to various problems arising in mathematical physics [46, 41, 181, 201, 27], see the reviews [47, 188, 50, 51] and references therein.”
On Nonperiodic Euler Flows with Hölder Regularity (2014, methodology): “Beginning with the work of [14], the space of approximate solutions used to build continuous solutions to (E) consists of the solutions to the following underdetermined system known as the “Euler–Reynolds equations”:”
Non-uniqueness and h-Principle for Hölder-Continuous Weak Solutions of the Euler Equations (2016, methodology): “We also recall from [10, 3] the following geometric lemma: Lemma 6.”
Non–uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data (2018, background): “For details see [15], [9] for one side of the conjecture and [14], [1], [2], [3], [4], [11], [18] and [19] for the other side.”
Dissipative Euler Flows with Onsager‐Critical Spatial Regularity (2014, methodology): “k C k /: Another important ingredient is the following geometric lemma, also taken from [12].”
Global Ill‐Posedness of the Isentropic System of Gas Dynamics (2013, background): “One could speculate that, in analogy to what has been shown recently for the incompressible Euler equations, even a “piecewise Hölder regularity” might not be enough; see [2, 12, 14, 16] and in particular [8].”