Non-uniqueness of weak solutions to hyperviscous Navier-Stokes equations: on sharpness of J.-L. Lions exponent

DOI10.1007/s00526-020-01742-4zbMath1437.35542arXiv1808.07595OpenAlexW3020399848MaRDI QIDQ2180857

Edriss S. Titi, Tianwen Luo

Publication date: 15 May 2020

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.07595

zbMATH Keywords

Navier-Stokes equationsfractional hyperviscosity

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Fractional derivatives and integrals (26A33) Navier-Stokes equations (35Q30) Weak solutions to PDEs (35D30) Fractional partial differential equations (35R11)

Related Items (21)

Remarks on the non-uniqueness in law of the Navier-Stokes equations up to the J.-L. Lions' exponent ⋮ Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1 ⋮ Non-uniqueness in law for the Boussinesq system forced by random noise ⋮ Sharp nonuniqueness for the Navier-Stokes equations ⋮ Non-uniqueness of weak solutions to 3D magnetohydrodynamic equations ⋮ Weak solutions of ideal MHD which do not conserve magnetic helicity ⋮ NonUniqueness in Law for Two-Dimensional Navier--Stokes Equations with Diffusion Weaker than a Full Laplacian ⋮ Non-uniqueness of weak solutions to 2D hypoviscous Navier-Stokes equations ⋮ \(L^2\)-critical nonuniqueness for the 2D Navier-Stokes equations ⋮ On the weak solutions for the MHD systems with controllable total energy and cross helicity ⋮ Non‐uniqueness of Leray–Hopf solutions to the forced fractional Navier–Stokes equations in three dimensions, up to the J. L. Lions exponent ⋮ A note on energy equality for the fractional Navier-Stokes equations ⋮ Global existence and non-uniqueness for 3D Navier-Stokes equations with space-time white noise ⋮ Convex integration constructions in hydrodynamics ⋮ Nonunique Weak Solutions in Leray--Hopf Class for the Three-Dimensional Hall-MHD System ⋮ Non uniqueness of power-law flows ⋮ Lower and upper bounds of temporal decay for solutions to \(n\)-dimensional hyperviscous Navier-Stokes equations ⋮ Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature ⋮ Weak solutions of the three-dimensional hypoviscous elastodynamics with finite kinetic energy ⋮ Continuous Data Assimilation for the Three-Dimensional Navier--Stokes Equations ⋮ Nonuniqueness in law for stochastic hypodissipative Navier-Stokes equations

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