Article
Asymptotic behavior of solutions to barotropic vorticity equation on a sphere
Authors
Abstract
The behavior of a viscous incompressible fluid on a rotating sphere is described by the nonlinear barotropic vorticity equation (BVE). Conditions for the existence of a bounded set that attracts all BVE solutions are given. In addition, sufficient conditions are obtained for a BVE solution to be a global attractor. It is shown that, in contrast to the stationary forcing, the dimension of the global BVE attractor under quasiperiodic forcing is not limited from above by the generalized Grashof number.
Keywords
Barotropic vorticity equation on a sphere, global attractive set, global asymptotic stability, dimension of global attractor, 76D17, 76E20, 76U05, 39A14
Citation
Skiba, Y. N. (2020). Asymptotic behavior of solutions to barotropic vorticity equation on a sphere. Applied Mathematics and Nonlinear Sciences, 5(2), 229–238. https://doi.org/10.2478/amns.2020.2.00046
Y. N. Skiba, “Asymptotic behavior of solutions to barotropic vorticity equation on a sphere,” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 2, pp. 229–238, 2020, doi: 10.2478/amns.2020.2.00046.
Skiba YN. Asymptotic behavior of solutions to barotropic vorticity equation on a sphere. Applied Mathematics and Nonlinear Sciences. 2020;5(2):229–238. doi:10.2478/amns.2020.2.00046.
Skiba, Y. N. (2020), ‘Asymptotic behavior of solutions to barotropic vorticity equation on a sphere’, Applied Mathematics and Nonlinear Sciences, 5(2), pp. 229–238. Available at: https://doi.org/10.2478/amns.2020.2.00046.
Skiba, Yuri N. “Asymptotic Behavior of Solutions to Barotropic Vorticity Equation on a Sphere.” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 2, 2020, pp. 229–238. https://doi.org/10.2478/amns.2020.2.00046.
Skiba, Yuri N. “Asymptotic Behavior of Solutions to Barotropic Vorticity Equation on a Sphere.” Applied Mathematics and Nonlinear Sciences 5, no. 2 (2020): 229–238. https://doi.org/10.2478/amns.2020.2.00046.
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Published by: Engineering Journals
