On the stationary Navier-Stokes problem in \(\mathbb {R}^3\): an approach in weighted Sobolev spaces

DOI10.1007/s00009-017-0940-8zbMath1377.35213OpenAlexW2617160447MaRDI QIDQ1674222

Mohamed Meslameni, Mondher Benjemaa, Hela Louati

Publication date: 1 November 2017

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-017-0940-8

zbMATH Keywords

Navier-Stokes equationsweighted Sobolev spacesOseen equationsvery weak solutionsfluid mechanic

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Stokes and related (Oseen, etc.) flows (76D07) Navier-Stokes equations (35Q30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items

On the stationary Navier-Stokes problem in \(\mathbb {R}^3\): an approach in weighted Sobolev spaces, Linearized Navier-Stokes equations with boundary conditions involving the pressure in an exterior domain of \(\mathbb{R}^3\), The scalar Oseen problem in two-dimensional exterior domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the stationary Navier-Stokes equations in exterior domains
• Linearized Navier-Stokes equations in \(\mathbb{R}^3\): an approach in weighted Sobolev spaces
• A class of solutions to stationary Stokes and Navier-Stokes equations with boundary data in \(W^{-1/q,q}\)
• Stationary Stokes, Oseen and Navier-Stokes equations with singular data
• Global \(L^ n\)-solution and its decay property for the Navier-Stokes equations in half-space \(R^ n_ +\)
• The stationary exterior 3D-problem of Oseen and Navier-Stokes equations in anisotropically weighted spaces
• Existence and regularity of very weak solutions of the stationary Navier-Stokes equations
• The stationary Navier-Stokes equations in 3D exterior domains. An approach in anisotropically weighted \(L^q\) spaces
• Dirichlet and Neumann exterior problems for the \(n\)-dimensional Laplace operator. An approach in weighted Sobolev spaces
• Asymptotic stability of the stationary solution to the compressible Navier-Stokes equations in the half space
• Solvability of the Navier-Stokes system with \(L^2\) boundary data
• On the stationary Navier-Stokes problem in \(\mathbb {R}^3\): an approach in weighted Sobolev spaces
• Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique
• Weak solutions of the stationary Navier-Stokes equations for a viscous incompressible fluid past an obstacle
• On the steady Oseen problem in the whole space
• On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems
• Espaces de Sobolev avec poids application au problème de Dirichlet dans un demi espace
• L^p-Solutions of the Steady-State Navier–Stokes Equations with Rough External Forces
• Espaces de Sobolev avec poids pour l'équation de Laplace dans le demi-espace
• On the Laplace operator and on the vector potential problems in the half‐space: an approach using weighted spaces
• ON STATIONARY SOLUTIONS OF THE PROBLEM OF FLOW PAST A BODY OF A VISCOUS INCOMPRESSIBLE FLUID
• Exterior Stationary Navier–Stokes Flows in 3D with Nonzero Velocity at Infinity: Asymptotic Behavior of the Second Derivatives of the Velocity