On the space-time regularity of \(C(0,T;L^n)\)-very weak solutions to the Navier-Stokes equations

DOI10.1016/j.na.2004.05.013zbMath1126.35038OpenAlexW2088165752MaRDI QIDQ1883461

Luigi C. Berselli, Giovanni Paolo Galdi

Publication date: 12 October 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2004.05.013

zbMATH Keywords

Navier-Stokes equationsinitial-boundary value problemvery weak solutionsspace-time regularity

Mathematics Subject Classification ID

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 (5)

A local smoothness criterion for solutions of the 3D Navier-Stokes equations ⋮ The regularity of very weak solutions to magneto-hydrodynamics equations ⋮ Energy equality for the tropical climate models ⋮ On the energy equality for the 3D Navier-Stokes equations ⋮ On the relation between very weak and Leray–Hopf solutions to Navier–Stokes equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global \(L^ n\)-solution and its decay property for the Navier-Stokes equations in half-space \(R^ n_ +\)
• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• On the singular set and the uniqueness of weak solutions of the Navier- Stokes equations
• Weak solutions of Navier-Stokes equations
• 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
• \(L_ q-L_ r\) estimates for solutions of the nonstationary Stokes equation in an exterior domain and the Navier-Stokes initial value problems in \(L_ q\) spaces
• The weight function approach to uniqueness of viscous flows in unbounded domains
• Abstract \(L^ p\) estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains
• Remarks on the Schrödinger operator with singular complex potentials
• Uniqueness theorems for the three dimensional Navier-Stokes system
• On the strong solvability of the Navier-Stokes equations
• Remarks on the preceding paper by M. Ben-Artzi ``Global solutions of two- dimensional Navier-Stokes and Euler equations
• Zur Regularitätstheorie der instationären Gleichungen von Navier-Stokes
• On uniqueness for the Navier--Stokes system in 3D-bounded Lipschitz domains.
• On the Navier-Stokes initial value problem. I
• On the spatial analyticity of solutions of the Navier-Stokes equations
• The initial value problem for the Navier-Stokes equations with data in L\(^p\)
• UNIQUENESS OF MILD SOLUTIONS OF THE NAVIER-STOKES SYSTEM IN LN
• Interior regularity of weak solutions of the time-dependent Navier-Stokes equation
• L_3,∞-solutions of the Navier-Stokes equations and backward uniqueness
• Une remarque sur l'analyticité des solutions milds des équations de Navier–Stokes dans
• On the analyticity and the unique continuation theorem for solutions of the Navier-Stokes equation
• Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet
• Uniqueness for mild solutions of Navier-Stokes equations in \(L^3(\mathbb{R}^3)\) and other limit functional spaces
• Solutions of incompressible Navier-Stokes equations in an exterior domain

This page was built for publication: On the space-time regularity of \(C(0,T;L^n)\)-very weak solutions to the Navier-Stokes equations