Finite dimensional global attractor for 3D MHD-\(\alpha\) models: a comparison

DOI10.1007/s00021-010-0041-yzbMath1294.35090OpenAlexW1998479494MaRDI QIDQ407419

Davide Catania

Publication date: 1 September 2014

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00021-010-0041-y

zbMATH Keywords

incompressible fluidglobal attractormagnetohydrodynamicsturbulence modelsMHD-\(\alpha\) modelmodified Leray-\(\alpha\) modelNavier-Stokes-\(\alpha\) modelregularizing MHDsimplified bardina model

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items (10)

On time-decay rates of strong solutions for the 3D magnetohydrodynamics equations with nonlinear damping ⋮ Decay characterization of solutions to a 3D magnetohydrodynamics-\(\alpha\) model ⋮ Well-posedness and attractors of the multi-dimensional hyperviscous magnetohydrodynamic equations ⋮ The global existence and analyticity of a mild solution to the 3D regularized MHD equations ⋮ Attractors of the 3D magnetohydrodynamics equations with damping ⋮ Global attractor for the Navier-Stokes equations with fractional deconvolution ⋮ Note on global regularity of 3D generalized magnetohydrodynamic-\(\alpha\) model with zero diffusivity ⋮ UPPER BOUNDS ON THE NUMBER OF DETERMINING MODES, NODES, AND VOLUME ELEMENTS FOR A 3D MAGENETOHYDRODYNAMIC-<i>α</i> 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 existence for a regularized magnetohydrodynamic-\(\alpha \) model
• Global existence for two regularized MHD models in three space-dimension
• Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models
• Infinite-dimensional dynamical systems in mechanics and physics
• Global classical solutions for MHD system
• Weak and classical solutions of the two-dimensional magnetohydrodynamic equations
• Mathematical results related to a two-dimensional magneto-hydrodynamic equations
• Some mathematical questions related to the mhd equations
• Analytical study of certain magnetohydrodynamic-α models
• On a Leray–α model of turbulence
• A modified-Leray-α subgrid scale model of turbulence
• The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory
• Global Cauchy problem for the 2-D magnetohydrodynamic-\(\alpha \) models with partial viscous terms

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