Analyticity and gevrey-class regularity for the second-grade fluid equations

DOI10.1007/s00021-010-0032-zzbMath1270.35370arXiv0912.1327OpenAlexW3103486693MaRDI QIDQ361150

Marius Paicu, Vlad C. Vicol

Publication date: 28 August 2013

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

Full work available at URL: https://arxiv.org/abs/0912.1327

zbMATH Keywords

global well-posednesssecond grade fluidsanalyticity radiusgevrey class

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Viscoelastic fluids (76A10) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Euler equations (35Q31)

Related Items

Almost global existence for the Prandtl boundary layer equations ⋮ Analytical smoothing effect of solution for the Boussinesq equations ⋮ Gevrey class regularity for the global attractor of a two-dimensional non-Newtonian fluid ⋮ Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise ⋮ Higher-order global regularity of an inviscid Voigt-regularization of the three-dimensional inviscid resistive magnetohydrodynamic equations ⋮ Wellposedness and convergence of solutions to a class of forced non-diffusive equations with applications ⋮ On the regularity and convergence of solutions to the 3D Navier-Stokes-Voigt equations ⋮ Vanishing diffusion limits and long time behaviour of a class of forced active scalar equations ⋮ Block-Diagonalization of ODEs in the Semiclassical Limit and $C^\omega$ versus $C^\infty$ Stationary Phase ⋮ Local-in-time solvability and space analyticity for the Navier-Stokes equations with BMO-type initial data ⋮ Local analyticity radii of solutions to the 3D Navier-Stokes equations with locally analytic forcing

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Oscillations and concentrations in weak solutions of the incompressible fluid equations
• The domain of analyticity of solutions to the three-dimensional Euler equations in a half space
• Global regularity for some classes of large solutions to the Navier-Stokes equations
• Analyticity of solutions for a generalized Euler equation
• Regularity of the global attractor and finite-dimensional behavior for the second grade fluid equations
• Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models
• Gevrey class regularity for the solutions of the Navier-Stokes equations
• Smallest scale estimates for the Navier-Stokes equations for incompressible fluids
• On the convergence rate of the Euler-\(\alpha \), an inviscid second-grade complex fluid, model to the Euler equations
• Loss of smoothness and energy conserving rough weak solutions for the \(3d\) Euler equations
• Propagation de l'analyticité locale pour les solutions de l'équation d'Euler. (Propagation of local analyticity for the solutions of the Euler equation)
• Periodic solutions of analytic functional differential equations are analytic
• Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade
• Existence and uniqueness of classical solutions of the equations of motion for second-grade fluids
• Weak and classical solutions of a family of second grade fluids
• On the regularity of the global attractor of a weakly damped, forced Korteweg-de Vries equation
• Regularity, determining modes and Galerkin methods.
• Global existence and uniqueness of solutions to the equations of second-grade fluids
• Further existence results for classical solutions of the equations of a second-grade fluid
• On the higher-order global regularity of the inviscid Voigt-regularization of three-dimensional hydrodynamic models
• Vorticity and Incompressible Flow
• On the radius of analyticity of solutions to the three-dimensional Euler equations
• Nonlinear Schrödinger evolution equations
• Analyticity of the attractor and the number of determining nodes for a weakly damped driven nonlinear Schrodinger equation
• Attractors for non-compact semigroups via energy equations
• Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems
• Editorial board
• On the dissipative scale for the Navier-Stokes equation
• Une remarque sur l'analyticité des solutions milds des équations de Navier–Stokes dans
• The Navier-Stokes-alpha model of fluid turbulence
• On the domain of analyticity for solutions of second order analytic nonlinear differential equations
• The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory