54 citations · 116 across the 17 of their papers we have counts for
18 papers
Poiseuille flow of hyperbolic Ericksen-Leslie system in dimension two
Geng Chen, Tao Huang, Xiang Xu +1
In this paper, we study the Poiseuille laminar flow in a tube for the full Ericksen-Leslie system. It is a parabolic-hyperbolic coupled system which may develop singularity in fini…
Global solutions of quasi-linear Hamiltonian mKdV equation
Fangchi Yan, Qingtian Zhang
We study the initial value problem of quasi-linear Hamiltonian mKdV equations. Our goal is to prove the global-in-time existence of a solution given sufficiently smooth, localized,…
Initial-boundary value problems for Poiseuille flow of nematic liquid crystal via full Ericksen-Leslie model
Geng Chen, Yanbo Hu, Qingtian Zhang
In this paper, we study the initial-boundary value problem for the Poiseuille flow of hyperbolic-parabolic Ericksen-Leslie model of nematic liquid crystals in one space dimension.…
Global solutions of quasi-geostrophic shallow-water fronts
Fangchi Yan, Qingtian Zhang
In this paper, we consider a family of piecewise constant solutions of the quasi-geostrophic shallow-water (QGSW) equation. We derive the contour dynamics equation of the QGSW fron…
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…
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…
Local wellposedness of an approximate equation for SQG fronts
John K. Hunter, Jingyang Shu, Qingtian Zhang
We prove local well-posedness in the Sobolev spaces , with , for an initial value problem for a nonlocal, cubically nonlinear, dispersive equation that…
On finite time BV blow-up for the p-system
Alberto Bressan, Geng Chen, Qingtian Zhang
The paper studies the possible blowup of the total variation for entropy weak solutions of the p-system, modeling isentropic gas dynamics. It is assumed that the density remains un…
No BV bounds for approximate solutions to p-system with general pressure law
Alberto Bressan, Geng Chen, Qingtian Zhang +1
For the p-system with large BV initial data, an assumption introduced in [3] by Bakhvalov guarantees the global existence of entropy weak solutions with uniformly bounded total var…
Unique Conservative Solutions to a Variational Wave Equation
Alberto Bressan, Geng Chen, Qingtian Zhang
Relying on the analysis of characteristics, we prove the uniqueness of conservative solutions to the variational wave equation . Given a solution $u(t,x)…
Uniqueness of Conservative Solutions to the Camassa-Holm Equation via Characteristics
Alberto Bressan, Geng Chen, Qingtian Zhang
The paper provides a direct proof the uniqueness of solutions to the Camassa-Holm equation, based on characteristics. Given a conservative solution , an equation is intro…
Lack of BV Bounds for Approximate Solutions to the p-system with Large Data
Alberto Bressan, Geng Chen, Qingtian Zhang
We consider front tracking approximate solutions to the p-system of isentropic gas dynamics. At interaction times, the outgoing wave fronts have the same strength as in the exact s…
Shock formation in the compressible Euler equations and related systems
Geng Chen, Robin Young, Qingtian Zhang
We prove shock formation results for the compressible Euler equations and related systems of conservation laws in one space dimension, or three dimensions with spherical symmetry.…
A blow-up criterion for 3-D compressible visco-elasticity
Yi Du, Chun Liu, QingTian Zhang
In this paper, we shall prove a blow-up criteria in terms of the upper bound of the density, deformation tensor and the gradient of deformation tensor for 3D compressible visco-ela…
Singularities of solutions to compressible Euler equations with vacuum
Zhen Lei, Yi Du, Qingtian Zhang
Presented are two results on the formation of finite time singularities of solutions to the compressible Euler equations in two and three space dimensions for isentropic, polytropi…