Remarks on the magnetic helicity and energy conservation for ideal magneto-hydrodynamics
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Publication:5444862
DOI10.1088/0951-7715/20/11/011zbMath1142.76062OpenAlexW2065470073MaRDI QIDQ5444862
Publication date: 26 February 2008
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1088/0951-7715/20/11/011
PDEs in connection with optics and electromagnetic theory (35Q60) PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05)
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Rigorous results on conserved and dissipated quantities in ideal MHD turbulence ⋮ A note on weak solutions of conservation laws and energy/entropy conservation ⋮ Non-uniqueness of weak solutions to 3D magnetohydrodynamic equations ⋮ Weak solutions of ideal MHD which do not conserve magnetic helicity ⋮ Energy conservation and regularity for the 3D magneto-hydrodynamics equations ⋮ Energy equality of MHD system under a weaker condition on magnetic field ⋮ 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 ⋮ Bounded solutions of ideal MHD with compact support in space-time ⋮ Convex integration constructions in hydrodynamics ⋮ Onsager's conjecture in bounded domains for the conservation of entropy and other companion laws ⋮ Conservation of energy for the Euler-Korteweg equations ⋮ Proof of Taylor's conjecture on magnetic helicity conservation ⋮ Energy and cross-helicity conservation for the three-dimensional ideal MHD equations in a bounded domain ⋮ Energy conservation for the weak solutions to the ideal inhomogeneous magnetohydrodynamic equations in a bounded domain ⋮ Energy equality for weak solutions to the 3D magnetohydrodynamic equations in a bounded domain ⋮ Dyadic models for ideal MHD
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