Transverse linear stability of line periodic traveling waves for water-wave models

Haragus, Mariana

Séminaire Laurent Schwartz — EDP et applications (2018-2019), Exposé no. 14, 12 p.

We review some recent results on transverse linear stability of line periodic traveling waves for the water-wave problem. A common feature of these results is that they can be obtained from two, rather simple, abstract stability criteria. While the first criterion gives sufficient conditions for linear instability, the second one, which is a counting result for unstable eigenvalues, leads to sufficient conditions for spectral stability. We restrict to waves of small amplitude bifurcating in four different parameter regimes. We focus on the simplest model equations, the Kadomtsev-Petviashvili I and II equations, and refer to existing works for other models, including the full Euler equations.

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