Analysis of a general family of regularized Navier-Stokes and MHD models

DOI10.1007/s00332-010-9066-xzbMath1207.35241arXiv0901.4412OpenAlexW1987869424MaRDI QIDQ613613

Michael Holst, Gantumur Tsogtgerel, Evelyn M. Lunasin

Publication date: 21 December 2010

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.4412

zbMATH Keywords

Euler equationturbulenceNavier-Stokes equationmagnetohydrodynamicsLeray-\(\alpha\)Navier-Stokes-Voight modelsimplified Bardina model

Mathematics Subject Classification ID

Statistical turbulence modeling (76F55) Navier-Stokes equations (35Q30) Direct numerical and large eddy simulation of turbulence (76F65) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Dynamical systems approach to turbulence (76F20)

Related Items

Mathematical results for some \(\alpha \) models of turbulence with critical and subcritical regularizations ⋮ Long-time dynamics of a regularized family of models for homogeneous incompressible two-phase flows ⋮ Stabilization of 3D Navier-Stokes-Voigt equations ⋮ Inertial manifolds for the hyperviscous Navier-Stokes equations ⋮ On the existence and long-time behavior of solutions to stochastic three-dimensional Navier–Stokes–Voigt equations ⋮ On the convergence of statistical solutions of the 3D Navier-Stokes-\(\alpha\) model as \(\alpha\) vanishes ⋮ Sharp upper and lower bounds of the attractor dimension for 3D damped Euler-Bardina equations ⋮ Unnamed Item ⋮ Decay characterization of solutions to a 3D magnetohydrodynamics-\(\alpha\) model ⋮ Data assimilation with model error: analytical and computational study for sabra shell model ⋮ Singular limits of Voigt models in fluid dynamics ⋮ Time optimal control of the unsteady 3D Navier-Stokes-Voigt equations ⋮ Uniform tail-ends estimates of the Navier-Stokes equations on unbounded channel-like domains ⋮ Discontinuous Galerkin approximations for an optimal control problem of three-dimensional Navier-Stokes-Voigt equations ⋮ Attractors of the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations with damping ⋮ Regularity and attractors for the three‐dimensional generalized Boussinesq system ⋮ Inertial manifolds for the 3D hyperviscous Navier–Stokes equation with L² force ⋮ On degrees of freedom of certain conservative turbulence models for the Navier-Stokes equations ⋮ Optimal Control of Time-Periodic Navier-Stokes-Voigt Equations ⋮ Large eddy simulation for turbulent flows with critical regularization ⋮ Feedback control of Navier-Stokes-Voigt equations by finite determining parameters ⋮ On the number of determining volume elements for 3D Navier-Stokes-Voigt equations ⋮ Bounds on energy and enstrophy for the 3D Navier-Stokes-\(\alpha\) and Leray-\(\alpha\) models ⋮ On a regularized family of models for homogeneous incompressible two-phase flows ⋮ Continuous data assimilation for the three-dimensional simplified Bardina model utilizing measurements of only two components of the velocity field ⋮ Upper bounds on the number of determining nodes for 3D Navier–Stokes–Voigt equations ⋮ On a regularized family of models for the full Ericksen-Leslie system ⋮ Time decay rate for two 3D magnetohydrodynamics- α models ⋮ On the regularity and convergence of solutions to the 3D Navier-Stokes-Voigt equations ⋮ On an accurate \(\alpha\) model for coarse mesh turbulent channel flow simulation ⋮ UPPER BOUNDS ON THE NUMBER OF DETERMINING MODES, NODES, AND VOLUME ELEMENTS FOR A 3D MAGENETOHYDRODYNAMIC-<i>α</i> MODEL ⋮ Asymptotic behavior of the solutions of the generalized globally modified Navier-Stokes equations ⋮ Stability and stabilization for the three-dimensional Navier-Stokes-Voigt equations with unbounded variable delay ⋮ Internal stabilization of stochastic 3D Navier-Stokes-Voigt equations with linearly multiplicative Gaussian noise ⋮ Trajectory attractors for 3D damped Euler equations and their approximation ⋮ Global attractor and determining modes for a hyperbolic MHD turbulence Model ⋮ Regularized family of models for incompressible Cahn-Hilliard two-phase flows ⋮ Inertial Manifolds via Spatial Averaging Revisited

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Determining finite volume elements for the 2D Navier-Stokes equations
• Gevrey regularity for the attractor of the 3D Navier-Stokes-Voight equations
• Viscosity versus vorticity stretching: global well-posedness for a family of Navier-Stokes-alpha-like models
• Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models
• Implementation of the LANS-\(\alpha\) turbulence model in a primitive equation ocean model
• Efficient form of the LANS-\(\alpha \) turbulence model in a primitive-equation ocean model
• Global regularity for a Birkhoff-Rott-\(\alpha \) approximation of the dynamics of vortex sheets of the 2D Euler equations
• On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model
• The Camassa-Holm equations and turbulence
• Direct numerical simulations of the Navier-Stokes alpha model
• Fluctuation effects on 3D Lagrangian mean and Eulerian mean fluid motion
• A note on regularity criterion for the 3D Boussinesq system with partial viscosity
• Global attractors and determining modes for the 3D Navier-Stokes-Voight equations
• Asymptotic analysis of the Navier-Stokes equations
• Inertial manifolds for nonlinear evolutionary equations
• Infinite-dimensional dynamical systems in mechanics and physics
• On the number of determining nodes for the 2D Navier-Stokes equations
• The anisotropic Lagrangian averaged Euler and Navier-Stokes equations
• A cheap Caffarelli-Kohn-Nirenberg inequality for the Navier-Stokes equation with hyper-dissipation
• On a well-posed turbulence model
• Length-scale estimates for the LANS-\(\alpha\) equations in terms of the Reynolds number
• On the construction of suitable solutions to the Navier-Stokes equations and questions regarding the definition of large eddy simulation
• A study of the Navier–Stokes-α model for two-dimensional turbulence
• Determining nodes, finite difference schemes and inertial manifolds
• On the Rate of Convergence of the Two-Dimensional α-Models of Turbulence to the Navier–Stokes Equations
• Regularity Criteria for the Viscous Camassa-Holm Equations
• Nonlinear Schrödinger–Helmholtz equation as numerical regularization of the nonlinear Schrödinger equation
• An inviscid regularization for the surface quasi‐geostrophic equation
• The LANS-α and Leray turbulence parameterizations in primitive equation ocean modeling
• Spectral scaling of the Leray-α model for two-dimensional turbulence
• Analytical study of certain magnetohydrodynamic-α models
• A connection between the Camassa–Holm equations and turbulent flows in channels and pipes
• A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows
• Regularization modeling for large-eddy simulation
• Numerical simulations of the Lagrangian averaged Navier–Stokes equations for homogeneous isotropic turbulence
• Global well-posedness for two modified-Leray-α-MHD models with partial viscous terms
• Estimates for the LANS-$\alpha$, Leray-$\alpha$ and Bardina models in terms of a Navier-Stokes Reynolds number
• Determining modes and fractal dimension of turbulent flows
• Multiplication dans les espaces de Besov
• Determining Projections and Functionals for Weak Solutions of the Navier-Stokes Equations
• Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems
• Camassa-Holm Equations as a Closure Model for Turbulent Channel and Pipe Flow
• Global well–posedness for the Lagrangian averaged Navier–Stokes (LANS–α) equations on bounded domains
• Partial regularity of suitable weak solutions of the navier-stokes equations
• Energy dissipation in body-forced turbulence
• On a Leray–α model of turbulence
• A modified-Leray-α subgrid scale model of turbulence
• Lagrangian Averaging for Compressible Fluids
• The Navier-Stokes-alpha model of fluid turbulence
• The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory