25 citations · 111 across the 15 of their papers we have counts for
16 papers
On the approximation of vorticity fronts by the Burgers-Hilbert equation
John K. Hunter, Ryan C. Moreno-Vasquez, Jingyang Shu +1
This paper proves that the motion of small-slope vorticity fronts in the two-dimensional incompressible Euler equations is approximated on cubically nonlinear timescales by a Burge…
Global solutions for a family of GSQG front equations
John K. Hunter, Jingyang Shu, Qingtian Zhang
We prove the global existence of solutions with small and smooth initial data of a nonlinear dispersive equation for the motion of generalized surface quasi-geostrophic (GSQG) fron…
Contour Dynamics for Surface Quasi-Geostrophic Fronts
John K. Hunter, Jingyang Shu, Qingtian Zhang
We use contour dynamics to derive equations of motion for infinite planar surface quasi-geostrophic (SQG) fronts, and show that it leads to the same result as a regularization proc…
Two-Front Solutions of the SQG Equation and its Generalizations
John K. Hunter, Jingyang Shu, Qingtian Zhang
The generalized surface quasi-geostrophic (GSQG) equations are transport equations for an active scalar that depend on a parameter . Special cases are the two-dimensional…
On the resonant reflection of weak, nonlinear sound waves off an entropy wave
John K. Hunter, Evan B. Smothers
We derive a degenerate quasilinear Schrödinger equation that describes the resonant reflection of very weak, nonlinear sound waves off a weak sawtooth entropy wave.
Global Solutions of a Surface Quasi-Geostrophic Front Equation
John K. Hunter, Jingyang Shu, Qingtian Zhang
We consider a nonlinear, spatially-nonlocal initial value problem in one space dimension on that describes the motion of surface quasi-geostrophic (SQG) fronts. We pro…