Jaime Angulo, Carlos Matheus, Didier Pilod
Published 2007-01-26, updated 2007-08-01Version 3
The objective of this paper is two-fold: firstly, we develop a local and global (in time) well-posedness theory for a system describing the motion of two fluids with different densities under capillary-gravity waves in a deep water flow (namely, a Schr\"odinger-Benjamin-Ono system) for \emph{low-regularity} initial data in both periodic and continuous cases; secondly, a family of new periodic traveling waves for the Schr\"odinger-Benjamin-Ono system is given: by fixing a minimal period we obtain, via the implicit function theorem, a smooth branch of periodic solutions bifurcating a Jacobian elliptic function called {\it dnoidal}, and, moreover, we prove that all these periodic traveling waves are nonlinearly stable by perturbations with the same wavelength.
Comments: 38 pages; typos corrected and global well-posedness theorem (in the continuous case) reworked to follow closely the arguments of Colliander, Holmes and Tzirakis
Global well-posedness for the Navier-Stokes-Boussinesq system with axisymmetric data
Global well-posedness and stability of electro-kinetic flows
Global well-posedness and scattering for the defocusing $H^{\frac12}$-subcritical Hartree equation in $\mathbb{R}^d$
![QR code for arXiv:math/0701786 [math.AP]](http://oss.arxitics.com/images/favicon.svg)