On the stability of solitary waves for the Ostrovsky equation. (English) Zbl 1144.35460
Summary: Considered herein is the stability of solitary-wave solutions of the Ostrovsky equation which is an adaptation of the Korteweg-de Vries equation widely used to describe the effect of rotation on the surface and internal solitary waves or the capillary waves. It is shown that the ground state solitary waves are global minimizers of energy functionals with the constrained variational problem and are deduced to be nonlinearly stable for the small effect of rotation. The analysis makes frequent use of the variational properties of the ground states.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35B35 | Stability in context of PDEs |
| 35B60 | Continuation and prolongation of solutions to PDEs |
| 76B25 | Solitary waves for incompressible inviscid fluids |
| 76E07 | Rotation in hydrodynamic stability |
| 76M30 | Variational methods applied to problems in fluid mechanics |
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