Regularity of Solution to Axis-symmetric Navier-Stokes Equations with a Slightly Supercritical Condition

Abstract

Consider an axis-symmetric suitable weak solution of 3D incompressible Navier-Stokes equation with nontrivial swirl. If the solution satisfies a slightly supercritical assumption, we will prove that v is regular. This extends the results of Chen-Strain-Tsai-Yau, Koch-Nadirashvili-Seregin-Sverak and Lei-Zhang where regularities under critical assumptions were proven.

40pages

References in corpus (4)

• On the loss of continuity for super-critical drift-diffusion equations
• A Liouville Theorem for the Axially-symmetric Navier-Stokes Equations
• A Priori Bounds for the Vorticity of Axis Symmetric Solutions to the Navier-Stokes Equations
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Cited by in corpus (8)

• Quantitative regularity for the Navier-Stokes equations via spatial concentration
• Improved quantitative regularity for the Navier-Stokes equations in a scale of critical spaces
• Some Remarks on Regularity Criteria of Axially Symmetric Navier-Stokes Equations
• Regularity of Solutions to the Navier-Stokes equations in ${\dot{B}}_{\infty ,\infty }^{-1}$
• A Note On Local Regularity of Axisymmetric Solutions to the Navier-Stokes Equations
• A Slightly Supercritical Condition of Regularity of Axisymmetric Solutions to the Navier-Stokes Equations
• Mild criticality breaking for the Navier-Stokes equations
• A Review of results on axially symmetric Navier-Stokes equations, with addendum by X. Pan and Q. S. Zhang