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- W3012634414 abstract "In this paper, we derive asymptotic properties of both the velocity and the vorticity fields to the 3-dimensional axially symmetric Navier–Stokes equations at infinity under the generalized D-solution assumption [Formula: see text] for [Formula: see text]. We do not impose any zero or non-zero constant vector asymptotic assumption to the solution at infinity. Our results generalize those in [H. Choe and B. Jin, Asymptotic properties of axis-symmetric D-solutions of the Navier–Stokes equations, J. Math. Fluid Mech. 11(2) (2009) 208–232; S. Weng, Decay properties of axially symmetric D-solutions to the steady Navier–Stokes equations, J. Math. Fluid Mech. 20(1) (2018) 7–25; B. Carrillo, X. Pan and Q. S. Zhang, Decay and vanishing of some axially symmetric D-solutions of the Navier–Stokes equations, J. Funct. Anal. 279(1) (2020) 108504], where the authors focused on the case [Formula: see text] and the velocity field approaches zero at infinity. Meanwhile, when [Formula: see text] and the velocity field approaches zero at infinity, our results coincide with the results in [H. Choe and B. Jin, Asymptotic properties of axis-symmetric D-solutions of the Navier–Stokes equations, J. Math. Fluid Mech. 11(2) (2009) 208–232; S. Weng, Decay properties of axially symmetric D-solutions to the steady Navier–Stokes equations, J. Math. Fluid Mech. 20(1) (2018) 7–25; B. Carrillo, X. Pan and Q. S. Zhang, Decay and vanishing of some axially symmetric D-solutions of the Navier–Stokes equations, J. Funct. Anal. 279(1) (2020) 108504]." @default.
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- W3012634414 date "2022-05-28" @default.
- W3012634414 modified "2023-10-11" @default.
- W3012634414 title "Asymptotic properties of generalized D-solutions to the stationary axially symmetric Navier–Stokes equations" @default.
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- W3012634414 doi "https://doi.org/10.1142/s0219199722500134" @default.
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