Remarks on local regularity of axisymmetric solutions to the 3D Navier–Stokes equations

DOI10.1080/03605302.2022.2070854zbMath1492.35219arXiv2201.01766OpenAlexW4229050650MaRDI QIDQ5095454

Hui Chen, Tai-Peng Tsai, Ting Zhang

Publication date: 8 August 2022

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.01766

zbMATH Keywords

Navier-Stokes equationspartial regularityMoser's iterationsuitable weak solutionaxisymmetric solutions

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations (35Q30) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03)

Related Items

Quantitative control of solutions to the axisymmetric Navier-Stokes equations in terms of the weak \(L^3\) norm, Correction to: Remarks on local regularity of axisymmetric solutions to the 3D Navier–Stokes equations, Global regular axially-symmetric solutions to the Navier-Stokes equations with small swirl, Finite speed axially symmetric Navier-Stokes flows passing a cone, Regularity criteria of the axisymmetric Navier-Stokes equations and Hardy-Sobolev inequality in mixed Lorentz spaces

Cites Work

• Unnamed Item
• Regularity of solutions to axisymmetric Navier-Stokes equations with a slightly supercritical condition
• A certain necessary condition of potential blow up for Navier-Stokes equations
• Regularity of 3D axisymmetric Navier-Stokes equations
• Liouville theorems for the Navier-Stokes equations and applications
• A Liouville theorem for the axially-symmetric Navier-Stokes equations
• On the interior regularity of weak solutions of the Navier-Stokes equations
• Regularity criterion to the axially symmetric Navier-Stokes equations
• Backward uniqueness for parabolic equations
• On axially symmetric flows in \(\mathbb{R}^3\)
• On partial regularity of suitable weak solutions to the three-dimensional Navier-Stokes equations
• Quantitative regularity for the Navier-Stokes equations via spatial concentration
• A slightly supercritical condition of regularity of axisymmetric solutions to the Navier-Stokes equations
• A note on local regularity of axisymmetric solutions to the Navier-Stokes equations
• Local regularity of axisymmetric solutions to the Navier-Stokes equations
• The global solutions of axisymmetric Navier-Stokes equations with anisotropic initial data
• An anisotropic partial regularity criterion for the Navier-Stokes equations
• Interior regularity criteria for suitable weak solutions of the Navier-Stokes equations
• Criticality of the axially symmetric Navier-Stokes equations
• Un teorema di unicita per le equazioni di Navier-Stokes
• On interior regularity criteria for weak solutions of the Navier-Stokes equations
• Improved quantitative regularity for the Navier-Stokes equations in a scale of critical spaces
• Fourier Analysis and Nonlinear Partial Differential Equations
• Lower Bound on the Blow-up Rate of the Axisymmetric Navier–Stokes Equations
• Lower Bounds on the Blow-Up Rate of the Axisymmetric Navier–Stokes Equations II
• A new proof of the Caffarelli-Kohn-Nirenberg theorem
• Partial regularity of suitable weak solutions of the navier-stokes equations
• Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet
• Quantitative bounds for critically bounded solutions to the Navier-Stokes equations