Weak Solutions with Decreasing Energy¶of Incompressible Euler Equations

By A. Shnirelman. 2000

158 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/424f55ceb0857df7371bc46a883b2bbd3dcd1251

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Dissipative Euler Flows and Onsager's Conjecture (2012, background): “The ones of [29, ?] are just square summable functions of time and space, whereas the example of [31] was the first to be in the energy space and the constructions of [12, 13] gave bounded solutions.”
Anomalous dissipation for 1/5-Hölder Euler flows (2015, methodology): “Weak solutions violating the energy equality have been constructed for a long time, starting with the seminal work of Scheffer [23], and Shnirelman [24].”
Dissipative continuous Euler flows (2012, background): “The first proof of the existence of a solution for which the total kinetic energy is a monotone decreasing function has been given by Shnirelman in [22].”
Particles and fields in fluid turbulence (2001, background): “Such a possibility was first noticed and exploited in a somewhat different context in the study of weak solutions of the Euler equations ( Brenier , 1989 ; Shnirelman , 1999 ) .”
h -Principle and Rigidity for C 1, α Isometric Embeddings (2012, unknown): “beyond L∞ (for previous work see [28–30]).”
The Euler equations as a differential inclusion (2007, background): “In another groundbreaking paper [22] Shnirelman proved the existence of L2 distributional solutions with f = 0 and energy which decreases in time.”
Convex integration and phenomenologies in turbulence (2019, methodology): “On the other hand, if one assumes an estimate on velocity increments in the inertial range, which amounts to ζ2 > 0, it was shown in [39] that weak limits of Leray solutions are weak solutions of the Euler equation. the Euler equations, yielding an alternative proof of Scheffer’s [173] and Schnirelm”
Dissipative Euler Flows with Onsager‐Critical Spatial Regularity (2014, background): “Shnirelman [24] and then for general dimension n 2 by the second and third author in [9, 10].”
On Admissibility Criteria for Weak Solutions of the Euler Equations (2007, background): “A simpler construction was later proposed by A. Shnirelman in [21].”
Cauchy Problem for Dissipative Hölder Solutions to the Incompressible Euler Equations (2013, methodology): “otal kinetic energy e. As a corollary, choosing eto be a monotone decreasing function, they obtain the existence of bounded dissipative solutions in all dimensions, thus extending Shnirelman’s result [Shn00]. Given a suitable initial datum v0 for which such solution exists, De Lellis and Sz´ekelyhid”