We prove spectral stability of smooth periodic travelling waves with respect to co-periodic perturbations. When the amplitude of the periodic wave is large, the wave has a peaked profile typical for surface waves. We prove linear and nonlinear instability of peaked periodic waves. The scope of this project is to develop new functional-analytical tools in the context of nonlinear stability of periodic waves.
Impact
The project has fundamental significance in the modern mathematical physics. Possible applications can be developed further in the context of physics of fluids.
Student Experience
The project involves the new PhD student at McMaster, Uyen Le. In 2016-2017, the project also involved MSc student at McMaster, Jin Li.
Countries
France, Netherlands
Impact
Research
Institutional Partner(s)
Delft University of Technology, Netherlands, University of Besancon, France
