Global existence for a regularized magnetohydrodynamic-\(\alpha \) model

DOI10.1007/s11565-009-0069-1zbMath1205.35220OpenAlexW2062333019MaRDI QIDQ626997

Davide Catania

Publication date: 19 February 2011

Published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11565-009-0069-1

zbMATH Keywords

incompressible fluidmagnetohydrodynamicsturbulence modelsregularizing MHDMHD-\(\alpha \) modelbardina model

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations (35Q30) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items (14)

Time decay rates for the generalized MHD-α equations in Sobolev–Gevrey spaces ⋮ Approximate continuous data assimilation of the 2D Navier-Stokes equations via the Voigt-regularization with observable data ⋮ The Cauchy problem for a Bardina-Oldroyd model to the incompressible viscoelastic flow ⋮ Finite dimensional global attractor for 3D MHD-\(\alpha\) models: a comparison ⋮ Global well-posedness of the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations ⋮ Attractors of the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping ⋮ The Oldroyd-\(\alpha\) model for the incompressible viscoelastic flow ⋮ Higher-order global regularity of an inviscid Voigt-regularization of the three-dimensional inviscid resistive magnetohydrodynamic equations ⋮ Note on global regularity of 3D generalized magnetohydrodynamic-\(\alpha\) model with zero diffusivity ⋮ Fully discrete finite element approximation of the 2D/3D unsteady incompressible magnetohydrodynamic-Voigt regularization flows ⋮ Regularity and convergence results of the velocity-vorticity-Voigt model of the 3D Boussinesq equations ⋮ Global attractor and determining modes for a hyperbolic MHD turbulence Model ⋮ Length-scale estimates for the 3D simplified Bardina magnetohydrodynamic model ⋮ Global regularity of 3D generalized incompressible magnetohydrodynamic-\(\alpha\) model

Cites Work

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• Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models
• Global classical solutions for MHD system
• Weak and classical solutions of the two-dimensional magnetohydrodynamic equations
• Compensated compactness and Hardy spaces
• Mathematical results related to a two-dimensional magneto-hydrodynamic equations
• Nonstationary flows of viscous and ideal fluids in \(R^3\)
• Some mathematical questions related to the mhd equations
• Analytical study of certain magnetohydrodynamic-α models
• Commutator estimates and the euler and navier-stokes equations
• A note on limiting cases of sobolev embeddings and convolution inequalities
• Nonlinear Schrödinger evolution equations
• Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
• Global Cauchy problem for the 2-D magnetohydrodynamic-\(\alpha \) models with partial viscous terms

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