Traveling wave solutions to a general incompressible Navier-Stokes-Fourier system with free boundary
ABSTRACT
In this talk, we will discuss traveling wave solutions to the free boundary problem associated to a generalized
Navier-Stokes Fourier system, which models a viscous, incompressible, heat-conducting fluid. The fluid is
assumed to occupy a horizontally infinite strip-like domain with flat rigid bottom and moving upper surface.
The fluid is acted upon by gravity as well as external sources of bulk force and boundary stress and an
external heat source. Additionally, we allow for temperature-dependent viscosity and capillary coefficients,
the latter of which gives rise to Marangoni stresses on the free surface. We develop a small data well-
posedness theory in Sobolev spaces that shows that if the sources of force, stress, and heat are small, then
there exists a unique solution depending continuously on these data.
