Weighted a priori estimates for the swirl component of the vorticity of the axisymmetric Navier-Stokes system

Abstract We study the axisymmetric Navier–Stokes equations. By invoking a two-dimensional Gagliardo–Nirenberg inequality, we could show r 7 2 − 4 p ω θ ∈ L ∞ ( 0 , T ; L p ( R 3 ) ) , for any 3 2 ≤ p ≤ 8 5 .

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