Convex integration and phenomenologies in turbulence

T Buckmaster, V Vicol - EMS Surveys in Mathematical Sciences, 2020 - ems.press
In this review article we discuss a number of recent results concerning wild weak solutions of
the incompressible Euler and Navier–Stokes equations. These results build on the …

A proof of Onsager's conjecture

P Isett - Annals of Mathematics, 2018 - projecteuclid.org
Abstract For any α\lt1/3, we construct weak solutions to the 3D incompressible Euler
equations in the class C_tC_x^α that have nonempty, compact support in time on R*T^3 and …

Onsager's conjecture for admissible weak solutions

T Buckmaster, C De Lellis, L Székelyhidi Jr… - arXiv preprint arXiv …, 2017 - arxiv.org
We prove that given any $\beta< 1/3$, a time interval $[0, T] $, and given any smooth energy
profile $ e\colon [0, T]\to (0,\infty) $, there exists a weak solution $ v $ of the three …

Dissipative continuous Euler flows

C De Lellis, L Székelyhidi - Inventiones mathematicae, 2013 - Springer
Dissipative continuous Euler flows | SpringerLink Skip to main content Advertisement
SpringerLink Log in Menu Find a journal Publish with us Search Cart 1.Home 2.Inventiones …

Global ill‐posedness of the isentropic system of gas dynamics

E Chiodaroli, C De Lellis… - Communications on Pure …, 2015 - Wiley Online Library
We consider the isentropic compressible Euler system in 2 space dimensions with pressure
law p (ρ)= ρ2 and we show the existence of classical Riemann data, ie pure jump …

Nonuniqueness of weak solutions to the SQG equation

T Buckmaster, S Shkoller, V Vicol - Communications on Pure …, 2019 - Wiley Online Library
We prove that weak solutions of the inviscid SQG equations are not unique, thereby
answering Open Problem 11 of De Lellis and Székelyhidi in 2012. Moreover, we also show …

Weak stability and closure in turbulence

C De Lellis, L Székelyhidi Jr - … Transactions of the …, 2022 - royalsocietypublishing.org
We survey recent results in the mathematical literature on the equations of incompressible
fluid dynamics, highlighting common themes and how they might contribute to the …

The ℎ-principle and the equations of fluid dynamics

C De Lellis, L Székelyhidi Jr - Bulletin of the American Mathematical …, 2012 - ams.org
The ℎ-principle and the equations of fluid dynamics Page 1 BULLETIN (New Series) OF THE
AMERICAN MATHEMATICAL SOCIETY Volume 49, Number 3, July 2012, Pages 347–375 S …

Convex integration constructions in hydrodynamics

T Buckmaster, V Vicol - Bulletin of the American Mathematical Society, 2021 - ams.org
We review recent developments in the field of mathematical fluid dynamics which utilize
techniques that go under the umbrella name convex integration. In the hydrodynamical …

A counterexample to well-posedness of entropy solutions to the compressible Euler system

E Chiodaroli - Journal of Hyperbolic Differential Equations, 2014 - World Scientific
We consider entropy solutions to the Cauchy problem for the isentropic compressible Euler
equations in the spatially periodic case. In more than one space dimension, the methods …