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math.AP2023
The traveling wave problem for the shallow water equations: well-posedness and the limits of vanishing viscosity and surface tension
Noah Stevenson, Ian Tice
In this paper we study solitary traveling wave solutions to a damped shallow water system, which is in general quasilinear and of mixed type. We develop a small data well-posedness…
math.AP2023
Well-posedness of the stationary and slowly traveling wave problems for the free boundary incompressible Navier-Stokes equations
Noah Stevenson, Ian Tice
We establish that solitary stationary waves in three dimensional viscous incompressible fluids are a generic phenomenon and that every such solution is a vanishing wave-speed limit…
math.AP2023
Well-posedness of the traveling wave problem for the free boundary compressible Navier-Stokes equations
Noah Stevenson, Ian Tice
We prove that traveling waves in viscous compressible liquids are a generic phenomenon. The setting for our result is a horizontally infinite, finite depth layer of compressible, b…