A regularity criterion for the solutions of 3D Navier-Stokes equations

DOI10.1016/j.jmaa.2008.05.027zbMath1147.35337OpenAlexW2039749880MaRDI QIDQ933500

Xicheng Zhang

Publication date: 21 July 2008

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.2008.05.027

zbMATH Keywords

regularity criterion3D Navier-Stokes equation

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)

Related Items (12)

Global regularity criterion for the dissipative systems modelling electrohydrodynamics involving the middle eigenvalue of the strain tensor ⋮ Two new regularity criteria for the 3D Navier-Stokes equations via two entries of the velocity gradient tensor ⋮ Blow-up criteria of the simplified Ericksen-Leslie system ⋮ A new regularity criterion for the 3D Navier-Stokes equations via two entries of the velocity gradient tensor ⋮ Conditional regularity for the 3D Navier-Stokes equations in terms of the middle eigenvalue of the strain tensor ⋮ A scaling invariant regularity criterion for the 3D incompressible magneto-hydrodynamics equations ⋮ Fractional Navier–Stokes regularity criterion involving the positive part of the intermediate eigenvalue of the strain matrix ⋮ A refined regularity criteria of weak solutions to the magneto-micropolar fluid equations ⋮ Blowup criteria of a dissipative system modeling electrohydrodynamics in sum spaces ⋮ Regularity criterion for 3D Boussinesq equations via partial horizontal derivatives of two velocity components ⋮ Some Serrin-type regularity criteria for weak solutions to the Navier-Stokes equations ⋮ Improvement of several regularity criteria for the Navier-Stokes equations

Cites Work

• On the interior regularity of weak solutions of the Navier-Stokes equations
• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations
• A new regularity criterion for the Navier-Stokes equations in terms of the gradient of one velocity component.
• The initial value problem for the Navier-Stokes equations with data in L\(^p\)
• 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
• Vorticity and Incompressible Flow
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