Mathematics Research Institute


Smooth and peaked waves in the reduced Ostrovsky equation

Dmitry Pelinovsky (McMaster University (Canada))

Fecha: 24/05/2019 11:00
Lugar: Sala de Grados I, Facultad de Ciencias
Grupo: GIR: Modelización, Teoría y Análisis Numérico en Problemas de Optimización y Ecuaciones de Evolución

Reduced Ostrovsky equation is a shallow-water model for a rotating fluid. It exhibits both global smooth solutions and wave breaking in a finite time. I will show how both solutions arise in the Cauchy problem depending on the size of initial data. Another family of solutions consists of travelling periodic waves parameterized by the wave speed. Peaked wave is a terminal point in the family of smooth periodic waves. I will explain why the smooth periodic waves are spectrally stable whereas the limiting peaked wave is spectrally and linearly unstable in the time evolution of the reduced Ostrovsky equation.