An optimal regularity criterion for the Navier-Stokes equations proved by a blow-up argument

DOI10.1016/j.nonrwa.2020.103207zbMath1455.35177OpenAlexW3089897395MaRDI QIDQ2215499

Zdeněk Skalák

Publication date: 13 December 2020

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2020.103207

zbMATH Keywords

Navier-Stokes equationsregularity criteriaconditional regularityrescaling procedure

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) Blow-up in context of PDEs (35B44)

Related Items (3)

Some new regularity criteria for the Navier-Stokes equations in terms of one directional derivative of the velocity field ⋮ Laminar flow in channels with porous walls: advancing the existence, uniqueness and approximation of solutions via fixed point approaches ⋮ A survey of geometric constraints on the blowup of solutions of the Navier-Stokes equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On vorticity directions near singularities for the Navier-Stokes flows with infinite energy
• Liouville theorems for the Navier-Stokes equations and applications
• Some new regularity criteria for the Navier-Stokes equations containing gradient of the velocity.
• A regularity criterion of Serrin-type for the Navier-Stokes equations involving the gradient of one velocity component
• Backward uniqueness for parabolic equations
• Sharp one component regularity for Navier-Stokes
• Regularity condition of the incompressible Navier-Stokes equations in terms of one velocity component
• An improved regularity criterion for the Navier-Stokes equations in terms of one directional derivative of the velocity field
• The end-point regularity criterion for the Navier-Stokes equations in terms of \(\partial_3 u\)
• Sufficient conditions for the regularity to the 3D Navier-Stokes equations
• Un teorema di unicita per le equazioni di Navier-Stokes
• Teoremi di inclusione per spazi di Sobolev non isotropi
• The Three-Dimensional Navier–Stokes Equations
• Navier-Stokes equations with regularity in one direction
• A note on a regularity criterion for the Navier–Stokes equations

This page was built for publication: An optimal regularity criterion for the Navier-Stokes equations proved by a blow-up argument