Periodic solutions of the Navier-Stokes equations with inhomogeneous boundary conditions

DOI10.1007/s11565-010-0108-yzbMath1205.35192OpenAlexW1991201073MaRDI QIDQ627019

Takahiro Okabe, Reinhard Farwig

Publication date: 19 February 2011

Published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11565-010-0108-y

zbMATH Keywords

Navier-Stokes equationsstrong solutionsweak solutionstime-periodic solutionsinhomogeneous boundary datareproductive property

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Periodic solutions to PDEs (35B10) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Weak solutions to PDEs (35D30)

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Cites Work

• Unnamed Item
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• Existence and periodicity of weak solutions of the Navier-Stokes equations in a time dependent domain
• Leray's problem on the stationary Navier-Stokes equations with inhomogeneous boundary data
• Weak solutions of Navier-Stokes equations
• On a larger class of stable solutions to the Navier-Stokes equations in exterior domains
• Existence, uniqueness and attainability of periodic solutions of the Navier-Stokes equations in exterior domains
• The Navier-Stokes equations in the weak-\(L^n\) space with time-dependent external force
• Generalized resolvent estimates for the Stokes system in bounded and unbounded domains
• Periodic solutions of the Navier-Stokes equations in unbounded domains
• A reproductive property of the Navier-Stokes equations
• On the equations rot\ v\(=g\) and div\ u\(=f\) with zero boundary conditions