Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	孙长贞, University of Franche-Comte
Inviter:	范晨捷
Title:	Transverse linear stability of one-dimensional solitary gravity water waves in a channel with finite depth
Language:	Chinese
Time & Venue:	2024.01.03 15:00-16:00 思源楼S615
Abstract:	The two dimensional gravity water wave system in a channel with finite depth admits a family of solitary waves (referred to as line solitary wave). The linear asymptotic stability of these line solitary water waves has been established by Pego and S.Sun, while the nonlinear stability remains open. Given the fact that the dispersion effect is stronger in higher dimension, it is anticipated that the nonlinear stability would be relatively easier to achieve in higher dimension. As a first step towards the nonlinear stability, we study the linear stability of line solitary waves for the three dimensional gravity water wave system—referred to as transverse linear stability. It is found that the small amplitude line solitary waves are transversely linear stable within the exponentially weighted space. More precisely, the semigroup of the linearized operator around the solitary waves decays exponentially within the subspace orthogonal to the space comprising continuous resonant modes. The key element of the proof relies on the uniform resolvent estimates, which are based on the semiclassical analysis, energy estimates together with KP-II approximation of the water waves in the long wave regime.