Qualitative properties of solutions to vorticity equation for a viscous incompressible fluid on a rotating sphere
| Autor: | Yuri N. Skiba |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Forcing (recursion theory)
Applied Mathematics General Mathematics 010102 general mathematics Mathematical analysis Grashof number General Physics and Astronomy 01 natural sciences Physics::Fluid Dynamics 010101 applied mathematics Arbitrarily large Vorticity equation Hausdorff dimension Attractor Uniqueness 0101 mathematics Laplace operator Mathematics |
| Zdroj: | Zeitschrift für angewandte Mathematik und Physik. 71 |
| ISSN: | 1420-9039 0044-2275 |
| Popis: | A nonlinear vorticity equation describing the behavior of a viscous incompressible fluid on a rotating sphere is considered. The viscosity term is modeled by a real degree of the Laplace operator. The smoothness of external forcing is established that guarantee the existence of a limited attractive set in the space of solutions. Theorems on the existence and uniqueness of non-stationary and stationary weak solutions are given. Sufficient conditions for the global asymptotic stability of solutions are obtained. An example is constructed that shows that, in contrast to the stationary forcing, the Hausdorff dimension of the global attractor generated by a quasiperiodic (in time) and polynomial (in space) forcing can be arbitrarily large, even if the generalized Grashof number is limited. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink