<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

Asymptotic behavior of solutions to barotropic vorticity equation on a sphere

Universidad Nacional Autónoma de México

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Asymptotic behavior of solutions to barotropic vorticity equation on a sphere"}

The behavior of a viscous incompressible fluid on a rotating sphere is described by the nonlinear barotropic vorticity equation (BVE). Conditions for the...

Asymptotic behavior of solutions to barotropic vorticity equation on a sphere

Published Online: Nov 10, 2020

Page range: 229 - 238

Received: Jan 13, 2020

Accepted: Feb 18, 2020

DOI: https://doi.org/10.2478/amns.2020.2.00046

Keywords
Barotropic vorticity equation on a sphere, global attractive set, global asymptotic stability, dimension of global attractor

© 2020 Yuri N. Skiba, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Asymptotic behavior of solutions to barotropic vorticity equation on a sphere

Published Online: Nov 10, 2020

Page range: 229 - 238

Received: Jan 13, 2020

Accepted: Feb 18, 2020

DOI: https://doi.org/10.2478/amns.2020.2.00046

KeywordsBarotropic vorticity equation on a sphere, global attractive set, global asymptotic stability, dimension of global attractor

© 2020 Yuri N. Skiba, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Barotropic vorticity equation on a sphere, global attractive set, global asymptotic stability, dimension of global attractor