Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuous dependence on the density for stratified steady water waves   There are two distinct regimes commonly used to model traveling waves in
stratified water: continuous stratification, where the density is smooth
throughout the fluid, and layer-wise continuous stratification, where the fluid
consists of multiple immiscible strata. The former is the more physically
accurate description, but the latter is frequently more amenable to analysis
and computation. By the conservation of mass, the density is constant along the
streamlines of the flow; the stratification can therefore be specified by
prescribing the value of the density on each streamline. We call this the
streamline density function.
  Our main result states that, for every smoothly stratified periodic traveling
wave in a certain small-amplitude regime, there is an $L^\infty$ neighborhood
of its streamline density function such that, for any piecewise smooth
streamline density function in that neighborhood, there is a corresponding
traveling wave solution. Moreover, the mapping from streamline density function
to wave is Lipschitz continuous in a certain function space framework. As this
neighborhood includes piecewise smooth densities with arbitrarily many jump
discontinues, this theorem provides a rigorous justification for the ubiquitous
practice of approximating a smoothly stratified wave by a layered one. We also
discuss some applications of this result to the study of the qualitative
features of such waves.

8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
9
The categories of this paper are: nlin