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math.AP2025
Desingularization of nondegenerate rotating vortex patches
Răzvan-Octavian Radu, Noah Stevenson
This paper analyzes the space of steady rotating solutions to the two-dimensional incompressible Euler equations nearby vortex patch solutions satisfying a natural nondegeneracy co…
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…