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math.AP2026
Global solutions to the Boussinesq equations and the planetary geostrophic approximation
Ryan Budahazy, Xin Liu
We investigate the three dimensional Boussinesq equations in the planetary geostrophic scale, where the buoyancy/gravity driven flow is near geostrophic balance in the large horizo…
math.AP2026
The traveling wave solutions of the 1D hyperbolic Keller-Segel equations
Xin Liu, William Kyle Barker
The goal of this paper is to investigate the traveling wave solutions with one-sided far field conditions for the one-dimensional hyperbolic Keller-Segel equations with quorum sens…
math.AP2026
Rigorous justification of the hydrostatic-incompressible approximation for weakly stratified isothermal flow
Quyuan Lin, Xin Liu
We consider the limit of small Mach number and small vertical-to-horizontal aspect ratio for the isothermal compressible Navier-Stokes system. In addition, we consider the scale in…