New a priori estimates for the axisymmetric Navier-Stokes system

Abstract We show in this paper that r d ω θ belongs to L ∞ ( 0 ; ∞ ; L 2 ( R 3 ) ) ∩ L 2 ( 0 , ∞ ; H 1 ( R 3 ) ) for any 3 2 d ≤ 3 . This improves previous a priori estimate significantly.

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