Proves global regularity for axisymmetric 3D Navier-Stokes flows with swirl by controlling near-axis source terms via circulation identities and Hardy estimates.
Lower bounds on the blow-up rate of the axisymmetric Navier-Stokes equations II
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abstract
Consider axisymmetric strong solutions of the incompressible Navier-Stokes equations in $\R^3$ with non-trivial swirl. Let $z$ denote the axis of symmetry and $r$ measure the distance to the z-axis. Suppose the solution satisfies either $|v (x,t)| \le C_*{|t|^{-1/2}} $ or, for some $\e > 0$, $|v (x,t)| \le C_* r^{-1+\epsilon} |t|^{-\epsilon /2}$ for $-T_0\le t < 0$ and $0<C_*<\infty$ allowed to be large. We prove that $v$ is regular at time zero.
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math.AP 1years
2026 1verdicts
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Global Regularity for Axisymmetric Navier--Stokes Flows with Swirl
Proves global regularity for axisymmetric 3D Navier-Stokes flows with swirl by controlling near-axis source terms via circulation identities and Hardy estimates.