A survey of geometric constraints on the blowup of solutions of the Navier-Stokes equation

DOI10.1007/s41808-021-00135-8zbMath1479.35628arXiv2111.00040OpenAlexW3209069194MaRDI QIDQ2061641

Yanyan Li

Publication date: 16 December 2021

Published in: Journal of Elliptic and Parabolic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.00040

zbMATH Keywords

Navier-Stokes equationregularity criteriafinite-time blowup

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Blow-up in context of PDEs (35B44)

Related Items (1)

Remarks on sparseness and regularity of Navier–Stokes solutions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Blow-up of critical Besov norms at a potential Navier-Stokes singularity
• A certain necessary condition of potential blow up for Navier-Stokes equations
• On the critical one component regularity for 3-D Navier-Stokes system: general case
• 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
• 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
• The role of eigenvalues and eigenvectors of the symmetrized gradient of velocity in the theory of the Navier--Stokes equations.
• Blow-up criteria for the Navier-Stokes equations in non-endpoint critical Besov spaces
• Regularity criterion for solutions to the Navier-Stokes equations in the whole 3D space based on two vorticity components
• The regularity criterion for the 3D Navier-Stokes equations involving end-point Prodi-Serrin type conditions
• Localized anisotropic regularity conditions for the Navier-Stokes equations
• Sharp one component regularity for Navier-Stokes
• An improved regularity criterion for the Navier-Stokes equations in terms of one directional derivative of the velocity field
• On the regularizing effect of the vorticity direction in incompressible viscous flows
• Improvement of some anisotropic regularity criteria for the Navier-Stokes equations
• On regularity criteria for the Navier-Stokes equations based on one directional derivative of the velocity or one diagonal entry of the velocity gradient
• Locally space-time anisotropic regularity criteria for the Navier-Stokes equations in terms of two vorticity components
• A regularity criterion for the Navier-Stokes equations via one diagonal entry of the velocity gradient
• Global well-posedness of 3-D anisotropic Navier-Stokes system with small unidirectional derivative
• The end-point regularity criterion for the Navier-Stokes equations in terms of \(\partial_3 u\)
• An optimal regularity criterion for the Navier-Stokes equations proved by a blow-up argument
• A regularity criterion for the Navier-Stokes equation involving only the middle eigenvalue of the strain tensor
• Global solutions of 3-d Navier-Stokes system with small unidirectional derivative
• Regularity criteria of the incompressible Navier-Stokes equations via only one entry of velocity gradient
• Sufficient conditions for the regularity to the 3D Navier-Stokes equations
• On the Navier-Stokes initial value problem. I
• Regularity criteria for the Navier-Stokes equations based on one or two items of the velocity gradient
• 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 refined regularity criterion for the Navier-Stokes equations involving one non-diagonal entry of the velocity gradient
• Some new regularity criteria for the Navier-Stokes equations in terms of one directional derivative of the velocity field
• On the critical one component regularity for 3-D Navier-Stokes system
• Navier-Stokes equations with regularity in one direction
• On the regularity of the solutions of the Navier–Stokes equations via one velocity component
• L_3,∞-solutions of the Navier-Stokes equations and backward uniqueness
• Critical regularity criteria for Navier–Stokes equations in terms of one directional derivative of the velocity
• Global regularity for solutions of the three dimensional Navier–Stokes equation with almost two dimensional initial data
• A locally anisotropic regularity criterion for the Navier–Stokes equation in terms of vorticity
• Well-posedness for the Navier-Stokes equations

This page was built for publication: A survey of geometric constraints on the blowup of solutions of the Navier-Stokes equation