Well-posedness and controllability of a nonlinear system for surface waves - Alex Montes; Ricardo Córdoba (Electronic Journal of Qualitative Theory of Differential Equations)
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.