Convergence of the 2D Euler-\(\alpha\) to Euler equations in the Dirichlet case: indifference to boundary layers

DOI10.1016/j.physd.2014.11.001zbMath1364.35277arXiv1403.5682OpenAlexW2170398852MaRDI QIDQ2356784

Aibin Zang, Edriss S. Titi, Helena J. Nussenzveig Lopes, Milton da Costa Lopes Filho

Publication date: 6 June 2017

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.5682

zbMATH Keywords

Euler equationsboundary layerhomogeneous Dirichlet boundary conditionsEuler-\(\alpha\) equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Theoretical approximation in context of PDEs (35A35) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Euler equations (35Q31)

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Cites Work

• Unnamed Item
• Unnamed Item
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• Unnamed Item
• Incompressible Euler as a limit of complex fluid models with Navier boundary conditions
• Nonlinear evolution equations and the Euler flow
• Vanishing viscosity limits and boundary layers for circularly symmetric 2D flows
• Approximation of 2D Euler equations by the second-grade fluid equations with Dirichlet boundary conditions
• Ordinary differential equations, transport theory and Sobolev spaces
• Vanishing viscosity limit for incompressible flow inside a rotating circle
• Global regularity for a Birkhoff-Rott-\(\alpha \) approximation of the dynamics of vortex sheets of the 2D Euler equations
• On the convergence rate of the Euler-\(\alpha \), an inviscid second-grade complex fluid, model to the Euler equations
• The Camassa-Holm equations and turbulence
• On the Euler equations of incompressible perfect fluids
• Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade
• Valeurs propres d'opérateurs définis par la restriction de systèmes variationnels à des sous-espaces
• The Euler-Poincaré equations and semidirect products with applications to continuum theories
• Zero viscosity limit for analytic solutions, of the Navier-Stokes equation on a half-space. I: Existence for Euler and Prandtl equations
• Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space. II: Construction of the Navier-Stokes solution
• Example of zero viscosity limit for two-dimensional nonstationary Navier- Stokes flows with boundary
• The convergence of the solutions of the Navier-Stokes equations to that of the Euler equations
• Boundary layer theory and the zero-viscosity limit of the Navier-Stokes equation
• Global well-posedness for the averaged Euler equations in two dimensions
• The geometry and analysis of the averaged Euler equations and a new diffeomorphism group
• Global existence and uniqueness of solutions to the equations of second-grade fluids
• Analysis on groups of diffeomorphisms of manifolds with boundary and the averaged motion of a fluid.
• Further existence results for classical solutions of the equations of a second-grade fluid
• Vanishing viscosity plane parallel channel flow and related singular perturbation problems
• THE VORTEX BLOB METHOD AS A SECOND-GRADE NON-NEWTONIAN FLUID
• A Kato type theorem on zero viscosity limit of Navier-Stokes flows
• An Introduction to the Mathematical Theory of the Navier-Stokes Equations
• Vanishing Viscosity Limits for a Class of Circular Pipe Flows
• On the Rate of Convergence of the Two-Dimensional α-Models of Turbulence to the Navier–Stokes Equations
• The Zero‐Viscosity Limit of the 2D Navier–Stokes Equations
• A connection between the Camassa–Holm equations and turbulent flows in channels and pipes
• Global regularity and convergence of a Birkhoff-Rott-α approximation of the dynamics of vortex sheets of the two-dimensional Euler equations
• On second grade fluids with vanishing viscosity
• The second grade fluid and averaged Euler equations with Navier-slip boundary conditions
• Camassa-Holm Equations as a Closure Model for Turbulent Channel and Pipe Flow
• Attractors for Navier-Stokes equations in domains with finite measure
• On the inviscid limit of the Navier-Stokes equations
• Boundary layers and the vanishing viscosity limit for incompressible 2D flow
• On the Inviscid Limit Problem of the Vorticity Equations for Viscous Incompressible Flows in the Half‐Plane
• On a Leray–α model of turbulence
• Asymptotic analysis of the eigenvalues of a Laplacian problem in a thin multidomain
• 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

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