Boussinesq equations and other
for small-amplitude long waves in nonlinear dispersive media. Part
the nonlinear theory.
In Part I of this work, a four-parameter family of Boussinesq systems
to describe the propagation of surface water waves. Similar systems
are expected to arise in other physical settings where the dominant
aspects of propagation are a balance between the nonlinear effects of
convection and the linear effects of frequency dispersion. In addition
to deriving these systems, we determined in Part I exactly which of them are
linearly well posed in various natural function classes. It was argued
that linear well-posedness is a natural necessary requirement for the
possible physical relevance of the model in question.
In the present article, it is shown that the first-order correct
that are linearly well posed are in fact locally nonlinearly well
posed. Moreover, in certain specific cases, global well-posedness is
established for physically relevant initial data.
In Part I, higher-order correct models were also derived. A preliminary
analysis of a promising subclass of these models shows them to be
Min Chen (firstname.lastname@example.org)