Existence and uniqueness for a Boussinesq system with a disordered forcing. (English) Zbl 1076.76012

Quintero, José R.; Muñoz, Juan C.

Methods Appl. Anal. 11, No. 1, 15-32 (2004).

Summary: We study the existence, uniqueness, regularity and continuous dependence on initial data of solutions for Cauchy problem associated with the coupled system of Boussinesq type equations forced by highly oscillatory smooth coefficients. The model describes two-way propagation of long water waves with small amplitude on the surface of a one-dimensional channel with rough bottom (disordered topography). The dependent variables in this model are the wave elevation \(\eta\) and the potential velocity \(u\) measured at the fixed depth \(Z_0=\sqrt{2/3}\).

MSC:

76B15	Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B03	Existence, uniqueness, and regularity theory for incompressible inviscid fluids
35Q35	PDEs in connection with fluid mechanics

Keywords:

Cauchy problem; long water waves; rough bottom