A proof of Onsager's conjecture

From MaRDI portal

Publication:1621947

Jump to:navigation, search

DOI10.4007/annals.2018.188.3.4zbMath1416.35194arXiv1608.08301OpenAlexW2962998285WikidataQ123141650 ScholiaQ123141650MaRDI QIDQ1621947

Philip Isett

Publication date: 12 November 2018

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.08301

zbMATH Keywords

regularity weak solutions Euler equations turbulence energy conservation energy dissipation fluid dynamics incompressible convex integration nonuniqueness anomalous dissipation

Mathematics Subject Classification ID

Weak solutions to PDEs (35D30) Isotropic turbulence; homogeneous turbulence (76F05) Fundamentals of turbulence (76F02) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Euler equations (35Q31) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

Energy conservation in the limit of filtered solutions for the 2D Euler equations ⋮ Dimension of the singular set of wild Hölder solutions of the incompressible Euler equations ⋮ From the Nash–Kuiper theorem of isometric embeddings to the Euler equations for steady fluid motions: Analogues, examples, and extensions ⋮ A fractal version of the Onsager’s conjecture: The 𝛽-model ⋮ Rigorous results on conserved and dissipated quantities in ideal MHD turbulence ⋮ Sufficient conditions for local energy conservation for the compressible Euler system ⋮ On Bounded Two-Dimensional Globally Dissipative Euler Flows ⋮ Typicality results for weak solutions of the incompressible Navier–Stokes equations ⋮ NonUniqueness in Law for Two-Dimensional Navier--Stokes Equations with Diffusion Weaker than a Full Laplacian ⋮ Approximating viscosity solutions of the Euler system ⋮ Nonuniqueness of solutions to the Euler equations with vorticity in a Lorentz space ⋮ Global-in-time probabilistically strong solutions to stochastic power-law equations: existence and non-uniqueness ⋮ Energy equality of the weak solutions to Navier-Stokes equations in the multiplier spaces ⋮ \(L^2\)-critical nonuniqueness for the 2D Navier-Stokes equations ⋮ Energy equality for the 3D inhomogeneous Navier-Stokes equations in Lorentz-Besov spaces ⋮ Energy equalities for the 2D reduced‐gravity two‐and‐a‐half layer system ⋮ Almost Everywhere Nonuniqueness of Integral Curves for Divergence-Free Sobolev Vector Fields ⋮ Energy conservation of weak solutions for the incompressible Euler equations via vorticity ⋮ On the failure of the chain rule for the divergence of Sobolev vector fields ⋮ Anomalous dissipation and lack of selection in the Obukhov-Corrsin theory of scalar turbulence ⋮ Regularity in time along the coarse scale flow for the incompressible Euler equations ⋮ Singular solutions of nonlinear hydrodynamic equations arising in turbulence theory ⋮ A class of supercritical/critical singular stochastic PDEs: existence, non-uniqueness, non-Gaussianity, non-unique ergodicity ⋮ The energy conservation of the Landau-Lifshitz-Bloch equation ⋮ An intermittent Onsager theorem ⋮ Energy conservation for weak solutions of incompressible fluid equations: the Hölder case and connections with Onsager's conjecture ⋮ Onsager's energy conservation of solutions for density-dependent Euler equations in \(\mathbb{T}^d\) ⋮ The role of density in the energy conservation for the isentropic compressible Euler equations ⋮ Boundary Vorticity Estimates for Navier–Stokes and Application to the Inviscid Limit ⋮ Semi-Lagrangian finite element exterior calculus for incompressible flows ⋮ Sharp Nonuniqueness of Solutions to Stochastic Navier–Stokes Equations ⋮ Rigidity and flexibility of isometric extensions ⋮ A general convex integration scheme for the isentropic compressible Euler equations ⋮ Dyadic models for fluid equations: a survey ⋮ On energy conservation for the hydrostatic Euler equations: an Onsager conjecture ⋮ Dissipative Euler Flows for Vortex Sheet Initial Data without Distinguished Sign ⋮ On the inviscid limit of the compressible Navier-Stokes equations near Onsager's regularity in bounded domains ⋮ On nonuniqueness and nonregularity for gradient flows of polyconvex functionals ⋮ Dissipation in Onsager's critical classes and energy conservation in \(BV \cap L^\infty\) with and without boundary ⋮ On the weak solutions for the MHD systems with controllable total energy and cross helicity ⋮ Energy conservation for the weak solutions to the 3D compressible nematic liquid crystal flow ⋮ Weak-strong uniqueness and vanishing viscosity for incompressible Euler equations in exponential spaces ⋮ Anomalous dissipation for the forced 3D Navier-Stokes equations ⋮ On the Helicity conservation for the incompressible Euler equations ⋮ Probabilistic descriptions of fluid flow: a survey ⋮ Energy equality for the tropical climate models ⋮ On Some Properties of the Curl Operator and Their Consequences for the Navier-Stokes System ⋮ Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier-Stokes equations: existence and nonuniqueness ⋮ Three-dimensional magnetohydrodynamics system forced by space-time white noise ⋮ On the 3D Navier-Stokes equations with a linear multiplicative noise and prescribed energy ⋮ A general sufficient criterion for energy conservation in the Navier–Stokes system ⋮ On symmetry breaking for the Navier-Stokes equations ⋮ Anomalous dissipation and spontaneous stochasticity in deterministic surface quasi-geostrophic flow ⋮ Global existence and non-uniqueness of 3D Euler equations perturbed by transport noise ⋮ Intermittency and lower dimensional dissipation in incompressible fluids ⋮ C^1,α isometric extensions ⋮ Regularity results for rough solutions of the incompressible Euler equations via interpolation methods ⋮ Regularity criterion on energy equality for compressible Cahn‐Hilliard‐Navier‐Stokes equations ⋮ Convex integration constructions in hydrodynamics ⋮ Ill posedness for the full Euler system driven by multiplicative white noise ⋮ Nonunique Weak Solutions in Leray--Hopf Class for the Three-Dimensional Hall-MHD System ⋮ Onsager's conjecture in bounded domains for the conservation of entropy and other companion laws ⋮ Infinitely many Leray–Hopf solutions for the fractional Navier–Stokes equations ⋮ Turbulence of generalised flows in two dimensions ⋮ Regularity in Time of Hölder Solutions of Euler and Hypodissipative Navier--Stokes Equations ⋮ Energy equality for the Navier–Stokes equations in weak-in-time Onsager spaces ⋮ On the conservation of energy in two-dimensional incompressible flows ⋮ Sufficient conditions for local scaling laws for stationary martingale solutions to the 3D Navier–Stokes equations ⋮ Energy equalities for compressible Navier–Stokes equations ⋮ An Onsager singularity theorem for Leray solutions of incompressible Navier–Stokes ⋮ A direct approach to nonuniqueness and failure of compactness for the SQG equation ⋮ Anomalous Dissipation, Anomalous Work, and Energy Balance for the Navier--Stokes Equations ⋮ Non–uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data ⋮ Weak entropy solutions to a model in induction hardening, existence and weak-strong uniqueness ⋮ A partial uniqueness result and an asymptotically sharp nonuniqueness result for the Zhikov problem on the torus ⋮ Remarks on the non-uniqueness in law of the Navier-Stokes equations up to the J.-L. Lions' exponent ⋮ Sharp energy regularity and typicality results for Hölder solutions of incompressible Euler equations ⋮ Renormalization and energy conservation for axisymmetric fluid flows ⋮ Nonuniqueness and existence of continuous, globally dissipative Euler flows ⋮ Localized mixing zone for Muskat bubbles and turned interfaces ⋮ Turbulent cascade direction and Lagrangian time-asymmetry ⋮ Onsager's conjecture on the energy conservation for solutions of Euler equations in bounded domains ⋮ Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1 ⋮ On uniqueness and helicity conservation of weak solutions to the electron-MHD system ⋮ Characterization of three-dimensional Euler flows supported on finitely many Fourier modes ⋮ Non-uniqueness in law for the Boussinesq system forced by random noise ⋮ On non-uniqueness of continuous entropy solutions to the isentropic compressible Euler equations ⋮ Energy conservation for solutions of incompressible viscoelastic fluids ⋮ Sharp nonuniqueness for the Navier-Stokes equations ⋮ Weak-strong uniqueness for the Navier-Stokes equation for two fluids with ninety degree contact angle and same viscosities ⋮ Non-uniqueness of weak solutions to 3D magnetohydrodynamic equations ⋮ Weak solutions of ideal MHD which do not conserve magnetic helicity ⋮ Non-uniqueness of Leray solutions of the forced Navier-Stokes equations ⋮ Energy conservation for the compressible Euler and Navier-Stokes equations with vacuum ⋮ On the interior regularity of weak solutions to the 2-D incompressible Euler equations ⋮ Energy conservation for the weak solutions to the 3D compressible magnetohydrodynamic equations of viscous non-resistive fluids in a bounded domain ⋮ Non-uniqueness of weak solutions to 2D hypoviscous Navier-Stokes equations ⋮ Non-uniqueness of weak solutions to hyperviscous Navier-Stokes equations: on sharpness of J.-L. Lions exponent ⋮ Sufficient conditions for dual cascade flux laws in the stochastic 2d Navier-Stokes equations ⋮ Kinetic statistics of scalar conservation laws with piecewise-deterministic Markov process data ⋮ Onsager's conjecture for the incompressible Euler equations in the Hölog spaces \(C^{0,\alpha}_\lambda (\bar{\Omega})\) ⋮ A sufficient condition for the Kolmogorov 4/5 law for stationary martingale solutions to the 3D Navier-Stokes equations ⋮ On self-similar solutions to the incompressible Euler equations ⋮ Stationary solutions and nonuniqueness of weak solutions for the Navier-Stokes equations in high dimensions ⋮ Energy equality in the isentropic compressible Navier-Stokes equations allowing vacuum ⋮ Energy conservation and regularity for the 3D magneto-hydrodynamics equations ⋮ Onsager's conjecture for subgrid scale \(\alpha\)-models of turbulence ⋮ On double Hölder regularity of the hydrodynamic pressure in bounded domains ⋮ Energy conservation for inhomogeneous incompressible and compressible Euler equations ⋮ \(L^2\)-density of wild initial data for the hypodissipative Navier-Stokes equations ⋮ On the extension of Onsager's conjecture for general conservation laws ⋮ Remarks on the emergence of weak Euler solutions in the vanishing viscosity limit ⋮ Very weak solutions to the two-dimensional Monge-Ampére equation ⋮ Non-conservative solutions of the Euler-\(\alpha\) equations ⋮ Very weak solutions of the Dirichlet problem for the two dimensional Monge-Ampère equation ⋮ Nonlinear open mapping principles, with applications to the Jacobian equation and other scale-invariant PDEs ⋮ Anomalous energy flux in critical \(L^p\)-based spaces ⋮ On nonuniqueness of Hölder continuous globally dissipative Euler flows ⋮ Construction of maximal functions associated with skewed cylinders generated by incompressible flows and applications ⋮ Energy conservation of the compressible Euler equations and the Navier-Stokes equations via the gradient ⋮ On the Rank-1 convex hull of a set arising from a hyperbolic system of Lagrangian elasticity ⋮ A uniqueness lemma with applications to regularization and incompressible fluid mechanics ⋮ Minimal acceleration for the multi-dimensional isentropic Euler equations ⋮ Analysis and numerical approximation of energy-variational solutions to the Ericksen-Leslie equations ⋮ Global existence and non-uniqueness for 3D Navier-Stokes equations with space-time white noise ⋮ Nonuniqueness of weak solutions to the Navier-Stokes equation ⋮ Convex integration solutions to the transport equation with full dimensional concentration ⋮ Bounded solutions of ideal MHD with compact support in space-time ⋮ Partial Regularity for the 3D Navier–Stokes Equations ⋮ Degraded mixing solutions for the Muskat problem ⋮ Analysis of a thermodynamically consistent Navier-Stokes-Cahn-Hilliard model ⋮ Nonuniqueness of Weak Solutions to the 3 Dimensional Quasi-Geostrophic Equations ⋮ Non-uniqueness for the transport equation with Sobolev vector fields ⋮ Remarks on the energy equality for the 3D Navier-Stokes equations ⋮ On the energy equality for the 3D Navier-Stokes equations ⋮ Non uniqueness of power-law flows ⋮ On the connection between Kolmogorov microscales and friction in pipe flows of viscoplastic fluids ⋮ An Onsager singularity theorem for turbulent solutions of compressible Euler equations ⋮ Positive solutions of transport equations and classical nonuniqueness of characteristic curves ⋮ Energy equality for weak solutions to Cahn-Hilliard/Navier-Stokes equations ⋮ Conservation of energy for the Euler-Korteweg equations ⋮ Energy conservation in 2-D density-dependent Euler equations with regularity assumptions on the vorticity ⋮ Nonuniqueness of weak solutions for the transport equation at critical space regularity ⋮ Non-uniqueness for the Euler equations up to Onsager's critical exponent ⋮ Proof of Taylor's conjecture on magnetic helicity conservation ⋮ \(C^{1, \alpha }\) isometric embeddings of polar caps ⋮ Maximally dissipative solutions for incompressible fluid dynamics ⋮ Regularity criterion on the energy conservation for the compressible Navier–Stokes equations ⋮ Higher Sobolev regularity of convex integration solutions in elasticity: the planar geometrically linearized hexagonal-to-rhombic phase transformation ⋮ Numerical evidence of anomalous energy dissipation in incompressible Euler flows: towards grid-converged results for the inviscid Taylor–Green problem ⋮ Weak-strong uniqueness for the Navier-Stokes equation for two fluids with surface tension ⋮ On solvability and ill-posedness of the compressible Euler system subject to stochastic forces ⋮ Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature ⋮ The energy measure for the Euler equations: the endpoint case ⋮ Energy conservation for the weak solutions to the ideal inhomogeneous magnetohydrodynamic equations in a bounded domain ⋮ Finite-time singularity formation for strong solutions to the axi-symmetric \(3D\) Euler equations ⋮ Hölder continuous solutions of Boussinesq equations ⋮ Onsager's conjecture with physical boundaries and an application to the vanishing viscosity limit ⋮ The vanishing viscosity limit for some symmetric flows ⋮ Visualization of the convex integration solutions to the Monge-Ampère equation ⋮ Convex integration arising in the modelling of shape-memory alloys: some remarks on rigidity, flexibility and some numerical implementations ⋮ Global well-posedness of the 3D Navier-Stokes equations perturbed by a deterministic vector field ⋮ Weak solutions of the three-dimensional hypoviscous elastodynamics with finite kinetic energy ⋮ Convex integration for diffusion equations and Lipschitz solutions of polyconvex gradient flows ⋮ Onsager's energy conservation for inhomogeneous Euler equations ⋮ Non-renormalized solutions to the continuity equation ⋮ Global Nash-Kuiper theorem for compact manifolds ⋮ Nonuniqueness in law for stochastic hypodissipative Navier-Stokes equations ⋮ Hölder regularity of helicity for the incompressible flows ⋮ A Kato-type criterion for vanishing viscosity near Onsager's critical regularity ⋮ Anomalous dissipation in passive scalar transport ⋮ Convex integration theory without integration ⋮ Energy conservation for the weak solutions to the incompressible inhomogeneous Euler-Korteweg equations ⋮ On singularities in the quaternionic Burgers equation

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:1621947&oldid=13926334"