Very weak solutions and the Fujita-Kato approach to the Navier-Stokes system in general unbounded domains
type: Item
instance of: scholarly article
title: Very weak solutions and the Fujita-Kato approach to the Navier-Stokes system in general unbounded domains
zbMATH Open document ID: 1333.35162
author: Reinhard Farwig
author: Paul Felix Riechwald
published in: NoDEA. Nonlinear Differential Equations and Applications
publication date: 2015-10-15T00:00:00Z
review text: The non-stationary Navier-Stokes system in a unbounded \(C^2\)-domain \(\Omega\subset \mathbb{R}^n\), \(n\geq 3\) is considered. After presenting the space \(\tilde{L}^q (\Omega)\), the definition of ``mild solution'' for the Navier-Stokes system with initial velocity \(\mathbf{u}_0\) is given. The main result is represented by the existence of mild solutions. A local uniqueness result is also obtained. A discussion concerning the relation between mild solutions and very weak solutions is provided.
reviewed by: Ruxandra Stavre
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 35D30
zbMATH DE Number: 6494620
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: Fujita-Kato method
zbMATH Keywords: mild solutions
zbMATH Keywords: very weak solutions
zbMATH Keywords: general unbounded domains
zbMATH Keywords: spaces \(\tilde{L}^q(\Omega)\)
MaRDI profile type: Publication
full work available at URL: s00030-015-0317-2
OpenAlex ID: W2021091669
cites work: Q4327845
cites work: Q4429175
cites work: Navier­Stokes Equations with Nonhomogeneous Dirichlet Data
cites work: On the strong solvability of the Navier-Stokes equations
cites work: Fourier Analysis and Nonlinear Partial Differential Equations
cites work: Q3784639
cites work: Elliptic boundary value problems in unbounded domains with noncompact and nonsmooth boundaries
cites work: A new class of weak solutions of the Navier-Stokes equations with nonhomogeneous data
cites work: An \(L^q\)-approach to Stokes and Navier-Stokes equations in general domains
cites work: Very weak solutions of the Navier-Stokes equations in exterior domains with nonhomogeneous data
cites work: On the Helmholtz decomposition in general unbounded domains
cites work: Q3437268
cites work: Q3601953
cites work: On the Stokes operator in general unbounded domains
cites work: Very weak solutions to the Navier-Stokes system in general unbounded domains
cites work: On the nonstationary Navier-Stokes systems
cites work: A class of solutions to stationary Stokes and Navier-Stokes equations with boundary data in \(W^{-1/q,q}\)
cites work: Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system
cites work: Solutions in \(L_ r\) of the Navier-Stokes initial value problem
cites work: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet
cites work: Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
cites work: \(H^{\infty}\)-calculus for the Stokes operator on unbounded domains
cites work: Interpolation of sum and intersection spaces of \(L^q\)-type and applications to the Stokes problem in general unbounded domains
cites work: Very weak solutions to the stationary Stokes and Stokes resolvent problem in weighted function spaces
cites work: The instationary Stokes equations in weighted Bessel-potential spaces
cites work: The instationary Navier-Stokes equations in weighted Bessel-potential spaces
cites work: Q2743226
cites work: Q4169288
DOI: 10.1007/S00030-015-0317-2
description: scientific article; zbMATH DE number 6494620