Regularity of weak solutions to the Navier-Stokes equations in exterior domains

DOI10.1007/s00030-010-0055-4zbMath1189.76115OpenAlexW1981810612MaRDI QIDQ976945

Reinhard Farwig, Christian Komo

Publication date: 16 June 2010

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-010-0055-4

zbMATH Keywords

weak solutionsexterior domaininstationary Navier-Stokes equationsvery weak solutionslocal in time regularitySerrin's class

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30)

Related Items (9)

Partial regularity of suitable weak solutions to the four-dimensional incompressible magneto-hydrodynamic equations ⋮ Interior regularity of weak solutions to the perturbed Navier-Stokes equations. ⋮ Regularity of weak solutions to 3D incompressible Navier-Stokes equations ⋮ On regularity of weak solutions to the instationary Navier-Stokes system: a review on recent results ⋮ Global existence of a weak solution to 3d stochastic Navier-Stokes equations in an exterior domain ⋮ Local Regularity Results for the Instationary Navier-Stokes Equations Based on Besov Space Type Criteria ⋮ Necessary and sufficient conditions for local strong solvability of the Navier-Stokes equations in exterior domains ⋮ Optimal initial value conditions for local strong solutions of the Navier–Stokes equations in exterior domains ⋮ Uniqueness criteria and strong solutions of the Boussinesq equations in completely general domains

Cites Work

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• Very weak solutions of the Navier-Stokes equations in exterior domains with nonhomogeneous data
• On energy inequality, smoothness and large time behavior in L 2 for weak solutions of the Navier-Stokes equations in exterior domains
• \(L_ q-L_ r\) estimates for solutions of the nonstationary Stokes equation in an exterior domain and the Navier-Stokes initial value problems in \(L_ q\) spaces
• Abstract \(L^ p\) estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains
• Generalized resolvent estimates for the Stokes system in bounded and unbounded domains
• Local in time regularity properties of the Navier-Stokes equations

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