Regularity Criterion to the axially symmetric Navier-Stokes Equations

الأصل · EN

Smooth solutions to the axially symmetric Navier-Stokes equations obey the following maximum principle:ruθ(r,z,t)ₗ∞≤ruθ(r,z,0)ₗ∞. We first prove the global regularity of solutions if ruθ(r,z,0)ₗ∞ or ruθ(r,z,t)ₗ∞₍ᵣ≤ ᵣ₀₎ is small compared with certain dimensionless quantity of the initial data. This result improves the one in Zhen Lei and Qi S. Zhang 1. As a corollary, we also prove the global regularity under the assumption that |ruθ(r,z,t)|≤| r|⁻³/²,∀0<r≤δ₀∈(0,1/2).