A refined regularity criterion for the Navier-Stokes equations involving one non-diagonal entry of the velocity gradient

DOI10.1016/j.jmaa.2017.04.049zbMath1369.35045OpenAlexW2608598074MaRDI QIDQ2627945

Dingxing Zhong, Xiantong Huang, Zujin Zhang

Publication date: 9 June 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.04.049

zbMATH Keywords

Navier-Stokes equationsregularity 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) Weak solutions to PDEs (35D30)

Related Items (13)

Global existence of weak solution and regularity criteria for the 2D Bénard system with partial dissipation ⋮ The application of anisotropic Troisi inequalities to the conditional regularity for the Navier–Stokes equations ⋮ The local regularity conditions for the Navier-Stokes equations via one directional derivative of the velocity ⋮ Remarks on regularity criteria for the 3d Navier-Stokes equations ⋮ The optimal regularity criterion for the Navier‐Stokes equations in terms of one directional derivative of the velocity ⋮ Some new multiplicative Sobolev inequalities with applications to the Navier–Stokes equations ⋮ Global regularity results for the 212 D magnetic Bénard system with mixed partial viscosity ⋮ The anisotropic regularity criteria for 3D Navier-Stokes equations involving one velocity component ⋮ On regularity criteria for the Navier-Stokes equations based on one directional derivative of the velocity or one diagonal entry of the velocity gradient ⋮ A survey of geometric constraints on the blowup of solutions of the Navier-Stokes equation ⋮ On a two components condition for regularity of the 3D Navier-Stokes equations under physical slip boundary conditions on non-flat boundaries ⋮ Regularity criteria of the incompressible Navier-Stokes equations via only one entry of velocity gradient ⋮ Regularity criteria for Navier-Stokes equations with slip boundary conditions on non-flat boundaries via two velocity components

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On anisotropic regularity criteria for the solutions to 3D Navier-Stokes equations
• Logarithmically improved regularity criteria for the Navier-Stokes and MHD equations
• Regularity criterion for weak solutions to the Navier-Stokes equations in terms of the pressure in the class
• The regularity criterion for 3D Navier-Stokes equations involving one velocity gradient component
• Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor
• Some new regularity criteria for the Navier-Stokes equations containing gradient of the velocity.
• On regularity criteria for the \(n\)-dimensional Navier-Stokes equations in terms of the pressure
• Two regularity criteria for the 3D MHD equations
• Extension criterion via two-components of vorticity on strong solutions to the 3D Navier-Stokes equations
• A new regularity class for the Navier-Stokes equations in \(\mathbb{R}^ n\)
• Remarks on regularity criteria for the Navier-Stokes equations via one velocity component
• Regularity criteria for the 3D MHD equations involving one current density and the gradient of one velocity component
• A new regularity criterion for the Navier-Stokes equations in terms of the gradient of one velocity component.
• Criteria for the regularity of the solutions to the Navier-Stokes equations based on the velocity gradient
• A regularity criterion for the tridimensional Navier-Stokes equations in term of one velocity component
• Sufficient conditions for the regularity to the 3D Navier-Stokes equations
• On the regularity of the solutions to the Navier-Stokes equations via the gradient of one velocity component
• Un teorema di unicita per le equazioni di Navier-Stokes
• Regularity criterion via two components of vorticity on weak solutions to the Navier-Stokes equations in \(\mathbb R^3\).
• A new regularity criterion for weak solutions to the Navier-Stokes equations
• On the critical one component regularity for 3-D Navier-Stokes system
• A note on the regularity of the solutions to the Navier-Stokes equations via the gradient of one velocity component
• A REGULARITY CRITERION FOR THE NAVIER–STOKES EQUATIONS IN TERMS OF ONE DIRECTIONAL DERIVATIVE OF THE VELOCITY FIELD
• Interior regularity of weak solutions of the time-dependent Navier-Stokes equation
• Navier-Stokes equations with regularity in one direction
• On the regularity of the solutions of the Navier–Stokes equations via one velocity component
• On a regularity criterion for the Navier–Stokes equations involving gradient of one velocity component
• Regularity criteria for the three-dimensional Navier-Stokes equations
• L_3,∞-solutions of the Navier-Stokes equations and backward uniqueness
• Remarks on regularity criterion for weak solutions to the Navier–Stokes equations in terms of the gradient of the pressure
• One component regularity for the Navier–Stokes equations
• 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

This page was built for publication: A refined regularity criterion for the Navier-Stokes equations involving one non-diagonal entry of the velocity gradient