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期刊论文
A priori bound on the velocity in axially symmetric Navier-Stokes equations
arXiv,-0001,(): | arXiv:1309.6625
Let v be the velocity of Leray-Hopf solutions to the axially symmetric three-dimensional Navier-Stokes equations. Under suitable conditions for initial values, we prove the following a priori bound |v(x,t)|≤Cr2|lnr|1/2, where r∈(0,1/2) is the distance from x to the z axis, and C is a constant depending only on the initial value. This provides a pointwise upper bound (worst case scenario) for possible singularities while the recent papers \cite{CSTY2} and \cite{KNSS} gave a lower bound. The gap is polynomial order 1 modulo a half log term.
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