Regularity and convergence results of the velocity-vorticity-Voigt model of the 3D Boussinesq equations

DOI10.1007/s10440-021-00453-yzbMath1477.35092OpenAlexW3213957811MaRDI QIDQ2064648

Yuan Pei

Publication date: 6 January 2022

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-021-00453-y

zbMATH Keywords

regularityvorticityglobal existenceBoussinesq equationsfluid dynamicsVoigt regularization

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Second-order parabolic systems (35K40) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)

Cites Work

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• Numerical approximation of the Voigt regularization for incompressible Navier-Stokes and magnetohydrodynamic flows
• Unconditional long-time stability of a velocity-vorticity method for the 2D Navier-Stokes equations
• On the local well-posedness and a Prodi-Serrin-type regularity criterion of the three-dimensional MHD-Boussinesq system without thermal diffusion
• Global existence for a regularized magnetohydrodynamic-\(\alpha \) model
• The stabilized extrapolated trapezoidal finite element method for the Navier-Stokes equations
• Determining finite volume elements for the 2D Navier-Stokes equations
• Global existence for two regularized MHD models in three space-dimension
• Review of incompressible fluid flow computations using the vorticity- velocity formulation
• 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
• On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model
• Velocity-vorticity-helicity formulation and a solver for the Navier-Stokes equations
• Invariant measures for the 3D Navier-Stokes-Voigt equations and their Navier-Stokes limit
• The 2D Boussinesq equations with vertical viscosity and vertical diffusivity
• The Camassa-Holm equations and turbulence
• Global attractors and determining modes for the 3D Navier-Stokes-Voight equations
• Infinite-dimensional dynamical systems in mechanics and physics.
• On well-posedness of a velocity-vorticity formulation of the stationary Navier-Stokes equations with no-slip boundary conditions
• Global well-posedness of the viscous Boussinesq equations
• Effective vorticity-velocity formulations for three-dimensional incompressible viscous flows
• On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models
• A compact difference scheme for the Navier-Stokes equations in vorticity-velocity formulation
• Continuous data assimilation applied to a velocity-vorticity formulation of the 2D Navier-Stokes equations
• Higher-order global regularity of an inviscid Voigt-regularization of the three-dimensional inviscid resistive magnetohydrodynamic equations
• Continuous data assimilation for a 2D Bénard convection system through horizontal velocity measurements alone
• Implicit for local effects and explicit for nonlocal effects is unconditionally stable
• Global well-posedness of the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations
• Global regularity for the two-dimensional anisotropic Boussinesq equations with vertical dissipation
• Global regularity for the 2D Boussinesq equations with partial viscosity terms
• Natural vorticity boundary conditions on solid walls
• Global well-posedness for the 2D Boussinesq system with anisotropic viscosity and without heat diffusion
• Simple finite element method in vorticity formulation for incompressible flows
• The Navier-Stokes-Voight model for image inpainting
• On Error Analysis for the 3D Navier–Stokes Equations in Velocity-Vorticity-Helicity Form
• Sensitivity computations of eddy viscosity models with an application in drag computation
• An inviscid regularization for the surface quasi‐geostrophic equation
• A connection between the Camassa–Holm equations and turbulent flows in channels and pipes
• On NAVIER-STOKES and KELVIN-VOIGT Equations in Three Dimensions in Interpolation Spaces
• Local existence and blow-up criterion for the Boussinesq equations
• Camassa-Holm Equations as a Closure Model for Turbulent Channel and Pipe Flow
• A 3D incompressible Navier-Stokes velocity-vorticity weak form finite element algorithm
• Finite element solution of the Navier–Stokes equations by a velocity–vorticity method
• On relaxation times in the Navier-Stokes-Voigt model
• On a Leray–α model of turbulence
• An accurate numerical solution algorithm for 3D velocity–vorticity Navier–Stokes equations by the DQ method
• A modified-Leray-α subgrid scale model of turbulence
• Semi‐implicit schemes for transient Navier–Stokes equations and eddy viscosity models
• The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory