On the regularity of flows with Ladyzhenskaya Shear-dependent viscosity and slip or non-slip boundary conditions

DOI10.1002/cpa.20036zbMath1075.35045OpenAlexW2167657437MaRDI QIDQ4676582

Hugo Beirão da Veiga

Publication date: 4 May 2005

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.20036

zbMATH Keywords

weak solutionsa priori estimateregularity up to the boundary

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularity of solutions to a non homogeneous boundary value problem for general Stokes systems in \(\mathbb R^n_+\)
• On the application of the homogenization theory to a class of problems arising in fluid mechanics
• Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition
• Study of coating flow by the finite element method
• Separating flow near a static contact line: Slip at a wall and shape of a free surface
• Stability of the rest state of a viscous incompressible fluid
• Slip with friction and penetration with resistance boundary conditions for the Navier-Stokes equations -- numerical tests and aspects of the implementation
• Interior regularity for solutions to the modified Navier-Stokes equations
• Regularity for Stokes and generalized Stokes systems under nonhomogeneous slip-type boundary conditions
• Espaces de Sobolev avec poids application au problème de Dirichlet dans un demi espace
• The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence
• A note on steady flow of fluids with shear dependent viscosity
• An existence result for fluids with shear dependent viscosity — Steady flows
• APPROXIMATION OF THE LARGER EDDIES IN FLUID MOTIONS II: A MODEL FOR SPACE-FILTERED FLOW
• EXISTENCE AND REGULARITY OF SOLUTIONS AND THE STABILITY OF THE REST STATE FOR FLUIDS WITH SHEAR DEPENDENT VISCOSITY
• Sur certaines équations paraboliques non linéaires
• Regularity of solutions of two-dimensional equations in fluid dynamics models with nonlinear viscosity

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