Well-posedness and controllability of a nonlinear system for surface waves

Abstract

In this paper we study the well-posedness for the periodic Cauchy problem and the internal controllability of a one-dimensional system that describes the propagation of long water waves with small amplitude in the presence of surface tension. The well-posedness is proved by using the Fourier transform restriction method and the controllability is proved by using the moment method.

Keywords

• nonlinear system
• water waves
• well-posedness
• bourgain spaces
• spectral analysis
• internal control