On regularity criteria for the \(n\)-dimensional Navier-Stokes equations in terms of the pressure

DOI10.1016/j.jde.2008.02.030zbMath1143.35081OpenAlexW2007993400MaRDI QIDQ925052

Jishan Fan, Song Jiang, GuoXi Ni

Publication date: 29 May 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.02.030

zbMATH Keywords

Navier-Stokes equationsmultiplier spacesBesov spacesMorrey spacesregularity criteria

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)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularity criteria in weak spaces for 3-dimensional Navier-Stokes equations in terms of the pressure.
• On the interior regularity of weak solutions of the Navier-Stokes equations
• Strong \(L^ p\)-solutions of the Navier-Stokes equation in \(R^ m\), with applications to weak solutions
• On the regularity of the pressure of weak solutions of Navier-Stokes equations
• Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system
• The weight function approach to uniqueness of viscous flows in unbounded domains
• Regularity criteria in terms of pressure for the 3-D Navier-Stokes equations in a generic domain
• A sufficient condition on the pressure for the regularity of weak solutions to the Navier-Stokes equations
• Zur Regularitätstheorie der instationären Gleichungen von Navier-Stokes
• Uniqueness for some Leray-Hopf solutions to the Navier-Stokes equations.
• A new regularity class for the Navier-Stokes equations in \(\mathbb{R}^ n\)
• On a regularity criterion in terms of the gradient of pressure for the Navier-Stokes equations in \(\mathbb R^N\)
• The initial value problem for the Navier-Stokes equations with data in L\(^p\)
• On interior regularity criteria for weak solutions of the Navier-Stokes equations
• On a Serrin-type regularity criterion for the Navier-Stokes equations in terms of the pressure
• Basis of Wavelets and Atomic Decompositions of H 1 (ℝ n ) and H 1 (ℝ n × ℝ n )
• Interior regularity of weak solutions of the time-dependent Navier-Stokes equation
• On partial regularity results for the navier-stokes equations
• On A Regularity Criterion Up to The Boundary for Weak Solutions of The Navier–Stokes Equations
• Regularity criteria involving the pressure for the weak solutions to the Navier-Stokes equations
• Partial regularity of suitable weak solutions of the navier-stokes equations
• L_3,∞-solutions of the Navier-Stokes equations and backward uniqueness
• Strong solutions of the Navier-Stokes equation in Morrey spaces
• On regularity criteria in terms of pressure for the Navier-Stokes equations in ℝ³
• Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet
• Regularity criterion in terms of pressure for the Navier-Stokes equations

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