Non-uniqueness of weak solutions to 3D magnetohydrodynamic equations
From MaRDI portal
Publication:2166061
DOI10.1016/j.matpur.2022.07.009zbMath1504.35235arXiv2112.10515OpenAlexW4226140456MaRDI QIDQ2166061
Deng Zhang, Zirong Zeng, Ya-Chun Li
Publication date: 23 August 2022
Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2112.10515
PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Magnetohydrodynamics and electrohydrodynamics (76W05) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Transport equations (35Q49)
Related Items (5)
Rigorous results on conserved and dissipated quantities in ideal MHD turbulence ⋮ On the weak solutions for the MHD systems with controllable total energy and cross helicity ⋮ Magnetic helicity, weak solutions and relaxation of ideal MHD ⋮ Refined conserved quantities criteria for the ideal MHD equations in a bounded domain ⋮ Weak solutions of the three-dimensional hypoviscous elastodynamics with finite kinetic energy
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Dissipative continuous Euler flows
- Dissipative Euler flows and Onsager's conjecture
- Wild solutions for 2D incompressible ideal flow with passive tracer
- Non-uniqueness for the transport equation with Sobolev vector fields
- On the interior regularity of weak solutions of the Navier-Stokes equations
- On admissibility criteria for weak solutions of the Euler equations
- Global regularity for a logarithmically supercritical hyperdissipative Navier-Stokes equation
- The Euler equations as a differential inclusion
- Onsager's conjecture on the energy conservation for solutions of Euler's equation
- Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD
- Generalized MHD equations.
- A proof of Onsager's conjecture
- Gagliardo-Nirenberg inequalities and non-inequalities: the full story
- Ill-posedness of Leray solutions for the hypodissipative Navier-Stokes equations
- Nonuniqueness of weak solutions to the Navier-Stokes equation
- Positive solutions of transport equations and classical nonuniqueness of characteristic curves
- Nonuniqueness of weak solutions for the transport equation at critical space regularity
- Global ill-posedness for a dense set of initial data to the isentropic system of gas dynamics
- Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1
- 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
- Convex integration and phenomenologies in turbulence
- Convex integration solutions to the transport equation with full dimensional concentration
- Bounded solutions of ideal MHD with compact support in space-time
- Proof of Taylor's conjecture on magnetic helicity conservation
- On solvability and ill-posedness of the compressible Euler system subject to stochastic forces
- Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space?
- Anomalous dissipation for \(1/5\)-Hölder Euler flows
- Stationary solutions and nonuniqueness of weak solutions for the Navier-Stokes equations in high dimensions
- Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions
- Regularity criteria for the generalized viscous MHD equations
- A new proof of partial regularity of solutions to Navier-Stokes equations
- Un teorema di unicita per le equazioni di Navier-Stokes
- Non-uniqueness of admissible weak solutions to compressible Euler systems with source terms
- \(C^1\) isometric imbeddings
- Weak solutions of ideal MHD which do not conserve magnetic helicity
- An Introduction to Magnetohydrodynamics
- h-Principle and Rigidity for C 1,α Isometric Embeddings
- High dimensionality and h-principle in PDE
- On Nash’s unique contribution to analysis in just three of his papers
- Some mathematical questions related to the mhd equations
- Onsager's Conjecture for Admissible Weak Solutions
- A new proof of the Caffarelli-Kohn-Nirenberg theorem
- L3,∞-solutions of the Navier-Stokes equations and backward uniqueness
- On global-in-time weak solutions to the magnetohydrodynamic system of compressible inviscid fluids
- 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
- Nonuniqueness of Weak Solutions to the SQG Equation
- Remarks on the magnetic helicity and energy conservation for ideal magneto-hydrodynamics
- Regularity Criteria for the Generalized MHD Equations
- Infinitely many Leray–Hopf solutions for the fractional Navier–Stokes equations
- Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet
- Non–uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data
- Magnetohydrodynamic Turbulence
- Well-posedness for the Navier-Stokes equations
This page was built for publication: Non-uniqueness of weak solutions to 3D magnetohydrodynamic equations
