Small data global solutions for the Camassa-Choi equations

Abstract

We consider solutions to the Cauchy problem for an internal-wave model derived by Camassa-Choi in a paper in Journal of Fluid Mechanics (1996). This model is a natural generalization of the Benjamin-Ono and Intermediate Long Wave equations in the case of weak transverse effects. We prove the existence and long-time dynamics of global solutions from small, smooth, spatially localized initial data on ${\mathbb{R}}^2$.

35 pages, 4 figures, comments welcome!

References in corpus (1)

• Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions

Cited by in corpus (2)

• Dispersive estimates for full dispersion KP equations
• Lie symmetry analysis and similarity solutions for the Camassa-Choi equations