A REGULARITY CRITERION FOR AXIALLY SYMMETRIC SOLUTIONS TO THE NAVIER-STOKES EQUATIONS

摘要

The axially symmetric solutions to the Navier-Stokes equations are studied. Assume that either the radial component (v_r) of the velocity belongs to L∞(O, T; L_3(Ω_0)) or v_r/r belongs to L∞(O,T; L_(3/2)(Ω_0)), where Ω_0 is a neighborhood of the axis of symmetry. Assume additionally that there exist subdomains Ω_k, k = 1,... , N, such that Ω_0 (∩) ∪k=1N Ωk, and assume that there exist constants α1, α2 such that either vrL∞（O，T;L3(Ωk_)）≤α1 orvr/rL∞（O，T;L3/2(Ωk_)）≤α2 fork= 1,... ,N. Then the weak solution becomes strong (v ∈ W(2 2,1)(Ω×(O,T)), ▽p∈L2(Ω×(O,T))). Bibliography: 28 titles.