Non-unique weak solutions in Leray-Hopf class of the 3D Hall-MHD system

Abstract

Non-unique weak solutions in Leray-Hopf class are constructed for the three dimensional magneto-hydrodynamics with Hall effect. We adapt the widely appreciated convex integration framework developed in a recent work of Buckmaster and Vicol for the Navier-Stokes equation, and with deep roots in a sequence of breakthrough papers for the Euler equation.

39 pages

Cited by in corpus (11)

• Stationary and discontinuous weak solutions of the Navier-Stokes equations
• Non-uniqueness of Weak Solutions to the 3D Quasi-Geostrophic Equations
• Dyadic models with intermittency dependence for the Hall MHD
• Derivation of the Hall-MHD equations from the Navier-Stokes-Maxwell equations
• Nonuniqueness of weak solutions for the transport equation at critical space regularity
• $L^2$-critical nonuniqueness for the 2D Navier-Stokes equations
• Anomalous dissipation of energy and magnetic helicity for the electron-MHD system
• Anomalous dissipation, anomalous work, and energy balance for smooth solutions of the Navier-Stokes equations
• Phenomenologies of intermittent Hall MHD turbulence
• Weak solutions of the three-dimensional hypoviscous elastodynamics with finite kinetic energy
• Global weak solutions to the density-dependent Hall-magnetohydrodynamics system