|
| A New Highly Nonlinear Equation Modelling Shallow-Water Waves with Constant Vorticity |
| |
| View Full Text View/Add Comment Download reader |
| KeyWord:Shallow-water waves, vorticity, shear flow, Besov spaces, blow-up |
| Author Name | Affiliation | | Yu Liu | School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China | | Xingxing Liu | School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China | | Min Li | School of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China |
|
| Hits: 40 |
| Download times: 5 |
| Abstract: |
| In this paper we apply the approach of formal asymptotic expansions and perturbation theory to derive a new highly nonlinear shallow-water model from the full governing equations for two dimensional incompressible fluid with constant vorticity. This approximate model is generated by introduction of a larger scaling than the Camassa-Holm one, which is shown to be optimal in the sense that there are no non-local terms appearing in free surface equation. Moreover, we establish the local well-posedness of the Cauchy problem in Besov spaces, and give a blow-up criterion, which improve the previous corresponding results in Sobolev spaces. |
|
|
|
