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math.AP2025
Hydrostatic bubbles of compressible fluid in an incompressible fluid
Juhi Jang, Ian Tice
We study stationary configurations of compressible barotropic fluids lying inside an incompressible fluid and acted upon by a constant gravitational field. Without gravity, it is a…
math.AP2025
Gravity driven traveling bore wave solutions to the free boundary incompressible Navier-Stokes equations
Noah Stevenson, Ian Tice
We give the first mathematical construction of two-dimensional traveling bore wave solutions to the free boundary incompressible Navier-Stokes equations for a single finite depth l…
math.AP2025
Stationary wave solutions to two dimensional viscous shallow water equations: theory of small and large solutions
Noah Stevenson, Ian Tice
We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing…