5 papers
Global Well-Posedness of Contact Lines: 2D Navier-Stokes Flow
Yan Guo, Ian Tice, Lei Wu +2
Based on the global a priori estimates in [Guo-Tice, J. Eur. Math. Soc. (2024)], we establish the well-posedness of a viscous fluid model satisfying the dynamic law for the contact…
Traveling wave solutions to a general incompressible Navier-Stokes-Fourier system with free boundary
Jae Ho Choi, Ian Tice
We study traveling wave solutions to the free boundary problem associated to a generalized Navier-Stokes Fourier system, which models a viscous, incompressible, heat-conducting flu…
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…
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…
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…