Potentials and transmission problems in weighted Sobolev spaces for anisotropic Stokes and Navier–Stokes systems with L∞ strongly elliptic coefficient tensor

DOI10.1080/17476933.2019.1631293zbMath1467.35131arXiv1902.09739OpenAlexW2953975179MaRDI QIDQ5205922

Mirela Kohr, Wolfgang L. Wendland, Sergey E. Mikhailov

Publication date: 17 December 2019

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.09739

zbMATH Keywords

well-posednesstransmission problemsanisotropic Stokes system\(L_\infty\) coefficientsanisotropic Navier-Stokes systems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) PDEs in connection with fluid mechanics (35Q35) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items

On the well-posedness of two boundary-domain integral equation systems equivalent to the Dirichlet problem for the Stokes system with variable viscosity, Sobolev spaces and \(\nabla\)-differential operators on manifolds. I: Basic properties and weighted spaces, On some mixed-transmission problems for the anisotropic Stokes and Navier-Stokes systems in Lipschitz domains with transversal interfaces, Non-homogeneous Dirichlet-transmission problems for the anisotropic Stokes and Navier-Stokes systems in Lipschitz domains with transversal interfaces, Stationary anisotropic Stokes, Oseen and Navier–Stokes systems: Periodic solutions in ℝⁿ, Dirichlet and transmission problems for anisotropic Stokes and Navier-Stokes systems with \(L_\infty\) tensor coefficient under relaxed ellipticity condition

Cites Work

• Variational views of stokeslets and stresslets
• Integral potential method for a transmission problem with Lipschitz interface in \(\mathbb{R}^{3}\) for the Stokes and Darcy-Forchheimer-Brinkman PDE systems
• Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient. I: Equivalence and invertibility
• Traces, extensions and co-normal derivatives for elliptic systems on Lipschitz domains
• \(L^p\)-weighted theory for Navier-Stokes equations in exterior domains
• A well-posed problem for the exterior Stokes equations in two and three dimensions
• An introduction to Sobolev spaces and interpolation spaces
• Boundary integral equations
• Analysis of direct boundary-domain integral equations for a mixed BVP with variable coefficient. II: Solution regularity and asymptotics
• Spectral theory and complex interpolation
• Spaces of Kudrjavcev type. I: Interpolation, embedding, and structure
• Flow of a liquid with an anisotropic viscosity tensor
• Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains
• Dirichlet and Neumann exterior problems for the \(n\)-dimensional Laplace operator. An approach in weighted Sobolev spaces
• Green functions of conormal derivative problems for stationary Stokes system
• Layer potentials and Poisson problems for the nonsmooth coefficient Brinkman system in Sobolev and Besov spaces
• The stationary Navier-Stokes system in nonsmooth manifolds: the Poisson problem in Lipschitz and \(C^{1}\) domains
• Variational approach for the Stokes and Navier-Stokes systems with nonsmooth coefficients in Lipschitz domains on compact Riemannian manifolds
• Theory and practice of finite elements.
• The inhomogeneous Dirichlet problem in Lipschitz domains
• Solution regularity and co-normal derivatives for elliptic systems with non-smooth coefficients on Lipschitz domains
• Nonlinear Neumann-transmission problems for Stokes and Brinkman equations on Euclidean Lipschitz domains
• The Robin problem for the Brinkman system and for the Darcy-Forchheimer-Brinkman system
• Fundamental solutions for stationary Stokes systems with measurable coefficients
• Analysis of segregated boundary-domain integral equations for BVPs with non-smooth coefficients on Lipschitz domains
• Extending Sobolev functions with partially vanishing traces from locally \(({\epsilon},{\delta})\)-domains and applications to mixed boundary problems
• Poisson problems for semilinear Brinkman systems on Lipschitz domains in \(\mathbb{R}^n\)
• Transmission problems for the Navier-Stokes and Darcy-Forchheimer-Brinkman systems in Lipschitz domains on compact Riemannian manifolds
• The Green function for the Stokes system with measurable coefficients
• Newtonian and single layer potentials for the Stokes system with \(L^\infty\) coefficients and the exterior Dirichlet problem
• Potential techniques and regularity of boundary value problems in exterior non-smooth domains
• Espaces de Sobolev avec poids application au problème de Dirichlet dans un demi espace
• The finite element method with Lagrangian multipliers
• An Augmented Mixed Finite Element Method for the Navier--Stokes Equations with Variable Viscosity
• ANALYSIS OF DIRECT SEGREGATED BOUNDARY-DOMAIN INTEGRAL EQUATIONS FOR VARIABLE-COEFFICIENT MIXED BVPs IN EXTERIOR DOMAINS
• Localized boundary-domain singular integral equations of Dirichlet problem for self-adjoint second-order strongly elliptic PDE systems
• Convection in Porous Media
• Elliptic and parabolic regularity for second- order divergence operators with mixed boundary conditions
• Pseudostress-velocity formulation for incompressible Navier-Stokes equations
• Finite Element Methods for Navier-Stokes Equations
• Boundary Integral Operators on Lipschitz Domains: Elementary Results
• Mixed and Hybrid Finite Element Methods
• Layer potentials for general linear elliptic systems
• THE STOKES PROBLEM IN ℝⁿ: AN APPROACH IN WEIGHTED SOBOLEV SPACES
• Weak solutions for the exterior Stokes problem in weighted Sobolev spaces
• The Green function for the mixed problem for the linear Stokes system in domains in the plane
• Layer Potential Analysis for Pseudodifferential Matrix Operators in Lipschitz Domains on Compact Riemannian Manifolds: Applications to Pseudodifferential Brinkman Operators
• Boundary Integral Solvers for an Evolutionary Exterior Stokes Problem
• ON THE OSEEN PROBLEM IN THREE-DIMENSIONAL EXTERIOR DOMAINS
• Navier-Stokes equations on Lipschitz domains in Riemannian manifolds.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item