DOI10.1023/A:1012984210582zbMath0995.35051arXivnlin/0103039WikidataQ63866247 ScholiaQ63866247MaRDI QIDQ5957842
Ciprian Foias, Edriss S. Titi, Darryl D. Holm
Publication date: 17 October 2002
Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/nlin/0103039
Averaged Lagrangians and the mean effects of fluctuations in ideal fluid dynamics,
Approximate continuous data assimilation of the 2D Navier-Stokes equations via the Voigt-regularization with observable data,
On the solvability of the Jeffreys-Oldroyd-\(\alpha\) model,
On the large time behavior of solutions of the alpha Navier-Stokes equations,
On the rate of convergence of the 2-D stochastic Leray-\(\alpha \) model to the 2-D stochastic Navier-Stokes equations with multiplicative noise,
An energy, momentum, and angular momentum conserving scheme for a regularization model of incompressible flow,
Well-posedness and convergence results for the 3D-Lagrange Boussinesq-\(\alpha\) system,
The Cauchy problem for a Bardina-Oldroyd model to the incompressible viscoelastic flow,
A stochastic variational approach to the viscous Camassa-Holm and Leray-alpha equations,
The Leray-\(\alpha\beta\)-deconvolution model: energy analysis and numerical algorithms,
Effect of hyperviscosity on the geometry of the vorticity,
Existence of solutions for the MHD-Leray-alpha equations and their relations to the MHD equations,
Analyticity and gevrey-class regularity for the second-grade fluid equations,
Gevrey class regularity and exponential decay property for Navier-Stokes-\(\alpha\) equations,
The Navier-Stokes-\(\alpha \beta\) equations as a platform for a spectral multigrid method to solve the Navier-Stokes equations,
Local null controllability of viscous Camassa-Holm equation,
Inertial manifolds for the hyperviscous Navier-Stokes equations,
Viscosity versus vorticity stretching: global well-posedness for a family of Navier-Stokes-alpha-like models,
On the convergence of statistical solutions of the 3D Navier-Stokes-\(\alpha\) model as \(\alpha\) vanishes,
The Hölder continuity of the solution map to the \(b\)-family equation in weak topology,
Global in time analysis and sensitivity analysis for the reduced NS-\(\alpha\) model of incompressible flow,
Analysis of a general family of regularized Navier-Stokes and MHD models,
Finite dimensional global attractor for 3D MHD-\(\alpha\) models: a comparison,
Regularity criteria for a Lagrangian-averaged magnetohydrodynamic-\(\alpha \) model,
On the convergence of the two-dimensional second grade fluid model to the Navier-Stokes equation,
Asymptotic behaviour of the three-dimensional \(\alpha\)-Navier-Stokes model with locally Lipschitz delay forcing terms,
On the 3-D stochastic magnetohydrodynamic-\(\alpha\) model,
On degrees of freedom of certain conservative turbulence models for the Navier-Stokes equations,
Convergence of global attractors of a 2D non-Newtonian system to the global attractor of the 2D Navier-Stokes system,
Weak solutions to stochastic 3D Navier-Stokes-\(\alpha \) model of turbulence: \(\alpha \)-asymptotic behavior,
Analysis of a large eddy simulation model based on anisotropic filtering,
A deconvolution enhancement of the Navier-Stokes-\({\alpha}{\beta}\) model,
On the structural stability of the Euler-Voigt and Navier-Stokes-Voigt models,
Continuous data assimilation algorithm for simplified Bardina model,
Orbital stability of peakons with nonvanishing boundary for CH and CH-\(\gamma \) equations,
A note on helicity conservation in Leray models of incompressible flow,
The asymptotic finite-dimensional character of a spectrally-hyperviscous model of 3D turbulent flow,
Regularization of the shock wave solution to the Riemann problem for the relativistic Burgers equation,
The regularized Boussinesq equations with partial dissipations in dimension two,
A note on Taylor-Eddy and Kovasznay solutions of NS-\(\alpha\)-deconvolution and Leray-\(\alpha\)-deconvolution models,
Peaked wave solutions of Camassa-Holm equation,
A numerical study of the Navier-Stokes-\(\alpha \beta \) model,
Going to new lengths: studying the Navier-Stokes-\(\alpha\beta\) equations using the strained spiral vortex model,
Bounds on energy and enstrophy for the 3D Navier-Stokes-\(\alpha\) and Leray-\(\alpha\) models,
Approximation of the trajectory attractor for a 3D model of incompressible two-phase-flows,
Remarks on global attractors for the 3D Navier-Stokes equations with horizontal filtering,
Numerical analysis and testing of a stable and convergent finite element scheme for approximate deconvolution turbulence models,
A phase field \(\alpha\)-Navier-Stokes vesicle-fluid interaction model: existence and uniqueness of solutions,
Global regularity for a Birkhoff-Rott-\(\alpha \) approximation of the dynamics of vortex sheets of the 2D Euler equations,
Global attractor for the Navier-Stokes equations with fractional deconvolution,
On questions of decay and existence for the viscous Camassa-Holm equations,
A rate of convergence for the LANS\(\alpha\) regularization of Navier-Stokes equations,
Introduction to special issue: ``Nonlinear partial differential equations in mathematical fluid dynamics, On 3D Navier-Stokes equations: regularization and uniqueness by delays, Large time behavior and convergence for the Camassa-Holm equations with fractional Laplacian viscosity, Global Cauchy problem for a Leray-\(\alpha\) model, Stochastic phase field \(\alpha \)-Navier-Stokes vesicle-fluid interaction model, On unique ergodicity in nonlinear stochastic partial differential equations, On the stochastic 3D Navier-Stokes-\(\alpha\) model of fluids turbulence, On the convergence rate of the Euler-\(\alpha \), an inviscid second-grade complex fluid, model to the Euler equations, Optimal control of the viscous generalized Camassa-Holm equation, A note on regularity criteria for the viscous Camassa-Holm equations in multiplier spaces, The Cauchy problem for the 2D magnetohydrodynamic-\(\alpha \) equations, Uniformly random attractor for the three-dimensional stochastic nonautonomous Camassa-Holm equations, Compactons in a general compressible hyperelastic rod, Blow-up, zero \(\alpha\) limit and the Liouville type theorem for the Euler-poincaré equations, Convergence of filtered weak solutions to the 2D Euler equations with measure-valued vorticity, Stochastic non-Newtonian fluid motion equations of a nonlinear bipolar viscous fluid, Existence of solutions and Gevrey class regularity for Leray-alpha equations, Stochastic variational formulations of fluid wave-current interaction, Stochastic geometric models with non-stationary spatial correlations in Lagrangian fluid flows, 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, Existence and linear approximation for the stochastic 3D magnetohydrodynamic-alpha model, Note on global regularity of 2D regularized MHD equations with zero magnetic diffusion, Modeling error of \(\alpha\)-models of turbulence on a two-dimensional torus, Estimates of the modeling error of the \(\alpha \)-models of turbulence in two and three space dimensions, Data assimilation for the Navier-Stokes-\(\alpha \) equations, The attractor on viscosity Degasperis-Procesi equation, Optimal control of the viscous Camassa-Holm equation, Approximate controllability of second-grade fluids, Upper semicontinuity of trajectory attractors for 3D incompressible Navier-Stokes equation, Boundary control of viscosity Degasperis-Procesi equation, Regularity and convergence results of the velocity-vorticity-Voigt model of the 3D Boussinesq equations, Geometry and curvature of diffeomorphism groups with \(H^1\) metric and mean hydrodynamics, Regularity of the global attractor and finite-dimensional behavior for the second grade fluid equations, Finite dimensional uniform attractors for the nonautonomous Camassa-Holm equations, The pullback attractors for the nonautonomous Camassa-Holm equations, Convergence of Galerkin solutions and continuous dependence on data in spectrally-hyperviscous models of 3D turbulent flow, Modelling the climate and weather of a 2D Lagrangian-averaged Euler-Boussinesq equation with transport noise, Lagrangian averaged stochastic advection by Lie transport for fluids, Nonlinear dispersion in wave-current interactions, Optimal control of the viscous weakly dispersive Degasperis-Procesi equation, Trajectory attractors for 3D damped Euler equations and their approximation, An interpretation of the Navier-Stokes-alpha model as a frame-indifferent Leray regularization, On \(\alpha\) Navier-Stokes equations on a bounded domain, Nonlinear balance and exchange of stability in dynamics of solitons, peakons, ramps/cliffs and leftons in a 1+1 nonlinear evolutionary PDE, Peaked wave solutions of CH-r equation, Exponential attractors for the 3D fractional-order Bardina turbulence model with memory and horizontal filtering, Theoretical and computational analysis of the thermal quasi-geostrophic model, On the convergence rates for the three‐dimensional filtered Boussinesq equations, On the approximation of turbulent fluid flows by the Navier-Stokes-\(\alpha\) equations on bounded domains, Stochastic inviscid Leray-\( \alpha\) model with transport noise: convergence rates and CLT, Hydrostatic limit of the Navier-Stokes-alpha model, The Navier-Stokes-alpha model of fluid turbulence, Global well-posedness of the two-dimensional horizontally filtered simplified Bardina turbulence model on a strip-like region, On attractor’s dimensions of the modified Leray-alpha equation, Energy conservation in the limit of filtered solutions for the 2D Euler equations, Solvability of thermoviscoelastic problem for Leray alpha-model, A note on the blowup criterion of the Lagrangian averaged Euler equations, On 3D Lagrangian Navier-Stokes \(\alpha\) model with a class of vorticity-slip boundary conditions, Instantaneous energy and enstrophy variations in Euler-alpha point vortices via triple collapse, Numerical analysis and computational comparisons of the NS-alpha and NS-omega regularizations, Defects in Liquid Crystal Flows, Existence and uniqueness of invariant measures of 3D stochastic MHD-αmodel driven by degenerate noise, Stochastic Euler-Poincaré reduction, Global attractor for the regularized Bénard problem, On the convergence of the uniform attractor of 2D NS-\(\alpha \) model to the uniform attractor of 2D NS system, Time Optimal Control Problem of the 3D Navier-Stokes-α Equations, The Navier-Stokes-alpha equation via forward-backward stochastic differential systems, Asymptotic Galerkin convergence and dynamical system results for the 3-D spectrally-hyperviscous Navier-Stokes equations on bounded domains, Global well-posedness of solutions for magnetohydrodynamics-\(\alpha\) model in \(\mathbb{R}^3\), Sharp upper and lower bounds of the attractor dimension for 3D damped Euler-Bardina equations, Data assimilation with model error: analytical and computational study for sabra shell model, Onsager's conjecture for subgrid scale \(\alpha\)-models of turbulence, Global well-posedness of the velocity-vorticity-Voigt model of the 3D Navier-Stokes equations, Well-posedness for incompressible fluid-solid interaction with vorticity, On the use of the notion of suitable weak solutions in CFD, A remark on weak-strong uniqueness for suitable weak solutions of the Navier-Stokes equations, Optimal decay rate for higher-order derivatives of the solution to the Lagrangian-averaged Navier-Stokes-\(\alpha\) equation in \(\mathbb{R}^3\), An optimal control problem for the Navier-Stokes-\(\alpha\) system, Decay characterization of solutions to the viscous Camassa–Holm equations, Estimates for the two-dimensional Navier–Stokes equations in terms of the Reynolds number, Analytical study of certain magnetohydrodynamic-α models, The Oldroyd-\(\alpha\) model for the incompressible viscoelastic flow, ON THE STOCHASTIC 3D-LAGRANGIAN AVERAGED NAVIER–STOKES α-MODEL WITH FINITE DELAY, Optimal control of the viscous Degasperis-Procesi equation, Global solutions to the Navier-Stokes-\({\bar \omega}\) and related models with rough initial data, Uniform time of existence of the smooth solution for 3D Euler-α equations with periodic boundary conditions, Optimal Solution for the Viscous Modified Camassa–Holm Equation, Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics, A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows, An optimal control problem of the 3D viscous Camassa–Holm equations, ON THE HIGH ACCURACY NS-ALPHA-DECONVOLUTION TURBULENCE MODEL, Global regularity and convergence of a Birkhoff-Rott-α approximation of the dynamics of vortex sheets of the two-dimensional Euler equations, Asymptotic behaviour of the three-dimensional \(\alpha \)-Navier-Stokes model with delays, Space-time decay estimates of solutions to 3D incompressible viscous Camassa-Holm equations, Navier-Stokes-alpha model with temperature-dependent viscosity, High-order Galerkin convergence and boundary characteristics of the 3-D Navier-Stokes equations on intervals of regularity, Theory for the rotational deconvolution model of turbulence with fractional regularization, Convergence for a Splitting-Up Scheme for the 3D Stochastic Navier-Stokes-α Model, On a regularization of a scalar conservation law with discontinuous coefficients, Quantum kinematics of bosonic vortex loops, NEW BOUNDED TRAVELING WAVES OF CAMASSA–HOLM EQUATION, On the global boundary stabilization of the Camassa-Holm equation, Time decay rate for two 3D magnetohydrodynamics- α models, A family of new, high order NS-\(\alpha \) models arising from helicity correction in Leray turbulence models, Higher-order global regularity of an inviscid Voigt-regularization of the three-dimensional inviscid resistive magnetohydrodynamic equations, Global well-posedness of the Cauchy problem for certain magnetohydrodynamic-α models, Convergence results for a class of spectrally hyperviscous models of 3-D turbulent flow, Gevrey class regularity for the viscous Camassa-Holm equations, Approximate deconvolution model in a bounded domain with vertical regularization, Stability of the Crank–Nicolson–Adams–Bashforth scheme for the 2D Leray‐alpha model, Intermittency and regularity issues in \(3D\) Navier-Stokes turbulence, Convergence analysis of the Navier–Stokes alpha model, Existence of smooth attractors for the Navier-Stokes-omega model of turbulence, Solitons and peakons of a nonautonomous Camassa-Holm equation, Convergence analysis and computational testing of the finite element discretization of the Navier-Stokes alpha model, An enhanced-physics-based scheme for the NS-α turbulence model, Dissipative solvability of an alpha model of fluid flow with memory, Vorticity dynamics and turbulence models for Large-Eddy Simulations, Length-scale estimates for the LANS-\(\alpha\) equations in terms of the Reynolds number, 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, Circulation and Energy Theorem Preserving Stochastic Fluids, On the uniform controllability for a family of non-viscous and viscous Burgers-α systems, Continuous data assimilation for the three-dimensional Navier–Stokes-α model, GENERALIZED KINK WAVES IN A GENERAL COMPRESSIBLE HYPERELASTIC ROD, On the emergence of the Navier-Stokes-α model for turbulent channel flows, Architecture of Approximate Deconvolution Models of Turbulence*, On the viscous Camassa-Holm equations with fractional diffusion, Logarithmically improved blow-up criterion for smooth solutions to the Leray-$\alpha $-magnetohydrodynamic equations, On the Rate of Convergence of the Two-Dimensional α-Models of Turbulence to the Navier–Stokes Equations, Global well posedness and limit behavior of the solutions to the viscous Degasperis–Procesi equation, Discrete data assimilation for the three-dimensional Navier–Stokes-$\alpha $ model, Local Well-Posedness of the Anisotropic Lagrangian Averaged Navier–Stokes Equations with Stokes Projector Viscosity, On a dissipative form of Camassa–Holm equation, On the construction of suitable solutions to the Navier-Stokes equations and questions regarding the definition of large eddy simulation, Optimal feedback control for Leray and Navier-Stokes alpha models, Optimal solution for the viscous nonlinear dispersive wave equation, Strong solutions for the stochastic 3D LANS-α model driven by non-Gaussian Lévy noise, A study of the Navier–Stokes-α model for two-dimensional turbulence, Investigation of the weak solubility of the fractional Voigt alpha-model, The reduced order NS-αmodel for incompressible flow: theory, numerical analysis and benchmark testing, Time periodic solution of the viscous Camassa-Holm equation, On the α-Navier–Stokes–Vlasov and the α-Navier–Stokes–Vlasov–Fokker–Planck equations, The existence of solution for viscous Camassa-Holm equations on bounded domain in five dimensions, Length-scale estimates for the 3D simplified Bardina magnetohydrodynamic model, Model for laminar and turbulent flows of viscous and nonlinear viscous non-Newtonian fluids, Inertial Manifolds for Certain Subgrid-Scale $\alpha$-Models of Turbulence, Multiscale turbulence models based on convected fluid microstructure, Long-time behavior of a two-layer model of baroclinic quasi-geostrophic turbulence, WELL-POSEDNESS AND GLOBAL ATTRACTORS FOR LIQUID CRYSTALS ON RIEMANNIAN MANIFOLDS, Convergence of the 2D Euler-\(\alpha\) to Euler equations in the Dirichlet case: indifference to boundary layers, On the backward behavior of some dissipative evolution equations