Very weak solutions and the Fujita-Kato approach to the Navier-Stokes system in general unbounded domains

DOI10.1007/s00030-015-0317-2zbMath1333.35162OpenAlexW2021091669MaRDI QIDQ745899

Paul Felix Riechwald, Reinhard Farwig

Publication date: 15 October 2015

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

Full work available at URL: https://doi.org/10.1007/s00030-015-0317-2

zbMATH Keywords

Navier-Stokes equationsmild solutionsvery weak solutionsgeneral unbounded domainsFujita-Kato methodspaces \(\tilde{L}^q(\Omega)\)

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Weak solutions to PDEs (35D30)

Related Items (2)

Regularity criterion in terms of \textit{BMO}-type norm of the pressure gradient for the Navier-Stokes equations on unbounded domains ⋮ Maximal regularity of the Stokes system with Navier boundary condition in general unbounded domains

Cites Work

• The instationary Stokes equations in weighted Bessel-potential spaces
• Interpolation of sum and intersection spaces of \(L^q\)-type and applications to the Stokes problem in general unbounded domains
• A class of solutions to stationary Stokes and Navier-Stokes equations with boundary data in \(W^{-1/q,q}\)
• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• Very weak solutions of the Navier-Stokes equations in exterior domains with nonhomogeneous data
• On the Helmholtz decomposition in general unbounded domains
• \(H^{\infty}\)-calculus for the Stokes operator on unbounded domains
• On the Stokes operator in general unbounded domains
• Very weak solutions to the stationary Stokes and Stokes resolvent problem in weighted function spaces
• Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system
• Solutions in \(L_ r\) of the Navier-Stokes initial value problem
• On the strong solvability of the Navier-Stokes equations
• The instationary Navier-Stokes equations in weighted Bessel-potential spaces
• Very weak solutions to the Navier-Stokes system in general unbounded domains
• An \(L^q\)-approach to Stokes and Navier-Stokes equations in general domains
• A new class of weak solutions of the Navier-Stokes equations with nonhomogeneous data
• On the nonstationary Navier-Stokes systems
• Fourier Analysis and Nonlinear Partial Differential Equations
• Elliptic boundary value problems in unbounded domains with noncompact and nonsmooth boundaries
• NavierStokes Equations with Nonhomogeneous Dirichlet Data
• Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet
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