An Interior Regularity Criterion for an Axially Symmetric Suitable Weak Solution to the Navier-Stokes Equations

摘要

We show that if V is an axially symmetric suitable weak solution to the Navier-Stokes equations (in the sense of L. Caffarelli, R. Kohn & L. Nirenberg - see [2]) such that either υ_ρ (the radial component of V) or υ_θ (the tangential component of V) has a higher regularity than is the regularity following from the definition of a weak solution in a sub-domain D of the time-space cylinder Q_T then all components of V are regular in D.