Sharp non-uniqueness of weak solutions to 3D magnetohydrodynamic equations: beyond the Lions exponent
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Publication:6581810
DOI10.1016/j.jfa.2024.110528zbMath1545.35117MaRDI QIDQ6581810
Deng Zhang, Ya-Chun Li, Zirong Zeng
Publication date: 1 August 2024
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Magnetohydrodynamics and electrohydrodynamics (76W05) Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)
Cites Work
- Global regularity for a class of generalized magnetohydrodynamic equations
- Dissipative continuous Euler flows
- Dissipative Euler flows and Onsager's conjecture
- Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces
- A fractional porous medium equation
- Non-uniqueness for the transport equation with Sobolev vector fields
- On admissibility criteria for weak solutions of the Euler equations
- Two regularity criteria for the 3D MHD equations
- The Euler equations as a differential inclusion
- Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD
- Generalized MHD equations.
- A proof of Onsager's conjecture
- Nonuniqueness of weak solutions to the Navier-Stokes equation
- Unique weak solutions of the non-resistive magnetohydrodynamic equations with fractional dissipation
- 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
- On the proof of Taylor's conjecture in multiply connected domains
- Wild solutions of the Navier-Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1
- Sharp nonuniqueness for the Navier-Stokes equations
- Non-uniqueness of weak solutions to 3D magnetohydrodynamic equations
- Non-uniqueness of Leray solutions of the forced Navier-Stokes equations
- 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
- Bounded solutions of ideal MHD with compact support in space-time
- Higher order commutator estimates and local existence for the non-resistive MHD equations and related models
- Proof of Taylor's conjecture on magnetic helicity conservation
- Discontinuity of weak solutions to the 3D NSE and MHD equations in critical and supercritical spaces
- 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
- On the regularity of weak solutions to the magnetohydrodynamic equations
- Onsager's conjecture almost everywhere in time
- The initial value problem for the Navier-Stokes equations with data in L\(^p\)
- On the movement of a space-filling viscous liquid
- Non-uniqueness of admissible weak solutions to compressible Euler systems with source terms
- Weak solutions of ideal MHD which do not conserve magnetic helicity
- An Introduction to Magnetohydrodynamics
- Dissipative Euler Flows with Onsager-Critical Spatial Regularity
- A General Fractional Porous Medium Equation
- 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
- The Three-Dimensional Navier–Stokes Equations
- L3,∞-solutions of the Navier-Stokes equations and backward uniqueness
- Rigorous results on conserved and dissipated quantities in ideal MHD turbulence
- The Generalized Caffarelli‐Kohn‐Nirenberg Theorem for the Hyperdissipative Navier‐Stokes System
- Convex integration constructions in hydrodynamics
- Nonunique Weak Solutions in Leray--Hopf Class for the Three-Dimensional Hall-MHD System
- Nonuniqueness of Weak Solutions to the SQG Equation
- Lectures on Navier-Stokes Equations
- Remarks on the magnetic helicity and energy conservation for ideal magneto-hydrodynamics
- Regularity Criteria for the Generalized MHD Equations
- Norm inflation for generalized magneto-hydrodynamic system
- 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
- Magnetohydrodynamic Turbulence
- \(L^2\)-critical nonuniqueness for the 2D Navier-Stokes equations
- An intermittent Onsager theorem
- Magnetic helicity, weak solutions and relaxation of ideal MHD
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Related Items (3)
Non-uniqueness for the compressible Euler-Maxwell equations ⋮ On two conserved quantities in the inviscid electron and Hall magnetohydrodynamic equations ⋮ Sharp non-uniqueness for the 3D hyperdissipative Navier-Stokes equations: beyond the Lions exponent
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