Existence theorem and regularity criteria for the generalized MHD equations

DOI10.1016/j.nonrwa.2009.03.017zbMath1191.35011OpenAlexW1964506541MaRDI QIDQ974580

Jia Yuan

Publication date: 3 June 2010

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2009.03.017

zbMATH Keywords

Besov spaceLittlewood-Paley theoryregularity criteriaBony's paraproduct decompositionfractional dissipative terms

Mathematics Subject Classification ID

Magnetohydrodynamics and electrohydrodynamics (76W05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Cites Work

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• Remarks on regularities for the 3D MHD equations
• On the interior regularity of weak solutions of the Navier-Stokes equations
• Space-time estimates in the Besov spaces and the Navier-Stokes equations
• On the regularity criterion of weak solution for the 3D viscous magneto-hydrodynamics equations
• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system
• Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD
• Viscous and inviscid magneto-hydrodynamics equations
• Generalized MHD equations.
• The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations
• A new regularity class for the Navier-Stokes equations in \(\mathbb{R}^ n\)
• A new Bernstein's inequality and the 2D dissipative quasi-geostrophic equation
• Regularity criteria for the generalized viscous MHD equations
• On the regularity of weak solutions to the magnetohydrodynamic equations
• Some mathematical questions related to the mhd equations
• Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
• L_3,∞-solutions of the Navier-Stokes equations and backward uniqueness
• Regularity Criteria for the Generalized MHD Equations
• Limiting case of the Sobolev inequality in BMO, with application to the Euler equations