Under a critical smallness condition on initial data, axisymmetric Navier-Stokes solutions with NHL boundary conditions in a finite cylinder remain globally regular.
von Wahl,Estimating ∇u by divu and curlu , Mathematical Methods in the Applied Sciences 15(2), 123–143 (1992)
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Global Regularity of Axisymmetric Navier-Stokes Equations with NHL Boundary Conditions under a Critical Smallness Condition
Under a critical smallness condition on initial data, axisymmetric Navier-Stokes solutions with NHL boundary conditions in a finite cylinder remain globally regular.