Mathematics – Analysis of PDEs
Scientific paper
2007-01-26
Mathematics
Analysis of PDEs
38 pages; typos corrected and global well-posedness theorem (in the continuous case) reworked to follow closely the arguments
Scientific paper
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.
Angulo Jaime
Matheus Carlos
Pilod Didier
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