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 …

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 …

[کتاب][B] Numerical analysis of compressible fluid flows

E Feireisl, M Lukáčová-Medviďová, H Mizerová, B She - 2021‏ - Springer
Many real-world problems involve fluids in motion. The goal of this book is to propose a new
approach to numerical analysis of the underlying nonlinear equations in the spirit of the …

Anomalous dissipation for the forced 3D Navier–Stokes equations

E Bruè, C De Lellis - Communications in Mathematical Physics, 2023‏ - Springer
In this paper, we consider the forced incompressible Navier–Stokes equations with
vanishing viscosity on the three-dimensional torus. We show that there are (classical) …

Non-uniqueness and h-principle for Hölder-continuous weak solutions of the Euler equations

S Daneri, L Székelyhidi Jr - Archive for Rational Mechanics and Analysis, 2017‏ - Springer
In this paper we address the Cauchy problem for the incompressible Euler equations in the
periodic setting. We prove that the set of Hölder 1/5-ε 1/5-ε wild initial data is dense in L^ 2 L …

Onsager's 'ideal turbulence'theory

G Eyink - Journal of Fluid Mechanics, 2024‏ - cambridge.org
In 1945–1949, Lars Onsager made an exact analysis of the high-Reynolds-number limit for
individual turbulent flow realisations modelled by incompressible Navier–Stokes equations …

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 …

[HTML][HTML] Mean-field limit of generalized Hawkes processes

J Chevallier - Stochastic Processes and their Applications, 2017‏ - Elsevier
We generalize multivariate Hawkes processes mainly by including a dependence with
respect to the age of the process, ie the delay since the last point. Within this class, we …

Construction of approximate entropy measure-valued solutions for hyperbolic systems of conservation laws

US Fjordholm, R Käppeli, S Mishra… - Foundations of …, 2017‏ - Springer
Entropy solutions have been widely accepted as the suitable solution framework for systems
of conservation laws in several space dimensions. However, recent results in De Lellis and …

Dissipative measure-valued solutions to the compressible Navier–Stokes system

E Feireisl, P Gwiazda… - Calculus of Variations …, 2016‏ - Springer
We introduce a new concept of dissipative measure-valued solution to the compressible
Navier–Stokes system satisfying, in addition, a relevant form of the total energy balance …