Long-Time Existence of Solutions to Boussinesq Systems

Source abstract

We establish the well-posedness on time scales of order $1/\epsilon$ of the Cauchy problem for a general class of Boussinesq systems modeling long-wave, small-amplitude gravity surface waves. Here $\epsilon$ is the small-parameter that measures the dispersive and nonlinear effects. Our proof relies on the use of the Nash--Moser theorem applied to a suitable transformation of the systems.