My research interest lies in nonlinear partial differential equations arising from physics, including
nonlinear hyperbolic conservation laws, nonlinear PDEs of mixed type
Maxwell-Chern-Simons equations in Gauge Theories
nonlinear variational wave equations
Publications
Existence of multiple solutions for the generalized Abelian Chern-Simons-Higgs model on a torus, preprint (with Jongmin Han)
Blow-up for a full variational sine-Gordon system, to appear in BKMS (with Qin Wang)
Singularity formation for a nonlinear variational sine-Gordon equation in a multidimensional space, Bull. Korean Math. Soc. 60 (2023), 1697-1704 (with Fengmei Qin and Qin Wang)
Topological multivortex solutions of the Maxwell-Chern-Simons-Higgs model with a background metric, Nonlinear Analysis TMA 235 (2023), 113345 (with Jongmin Han)
Existence of nontopological solutions for the generalized self-dual Maxwell-Chern-Simons-Higgs model, J. Math. Anal. Appl. 515 (2022) Article No. 126388
Topological solutions of the self-dual equations for the generalized Maxwell-Chern-Simons-Higgs model, J. Math. Anal. Appl. 504 (2021) Article No. 125327 (with Jongmin Han)
Shock diffraction problem by convex cornered wedges for isothermal gas, Acta Mathematica Scientia 41B (2021), 1130-1140 (with Qin Wang)
Subsonic solutions to a shock diffraction problem by a convex cornered wedge for the pressure gradient system, Comm. Pure Applied Analysis, 19 (2020), 4899-4920 (with Yinzheng Sun and Qin Wang)
Condensate solutions of the self-dual O(3) Maxwell-Chern-Simons-Higgs equations with symmetric vacua, Cal. Var. Partial Diff. Equations, 58 (2019), 135 (with Jongmin Han)
Improved existence results of solutions to the gravitational Maxwell gauged O(3) sigma model, Proceedings AMS, 144 (2016), 3499-3505
Energy conservative solutions to the system of full variational sine-Gordon equations in a unit sphere, J. Math. Physics 57, 021503 (2016) (with Qin Wang)
The regularity of sonic curves for the two-dimensional Riemann problems of the nonlinear wave system of Chaplygin gas, Discrete Contin. Dyn. Syst. A 36 (2016), 1661-1675 (with Qin Wang)
The regularity of semihyperbolic patches near sonic lines for the 2-D Euler system in gas dynamics, SIAM J. Math. Anal. 47 (2015), 2200-2219 (with Qin Wang and Yuxi Zheng)
Nontopological solutions in the self-dual Maxwell-Chern-Simons gauged O(3) sigma model, Nonlinear Analysis TMA 118 (2015), 22-40 (with Jongmin Han)
Vanishing pressure limits of Riemann solutions to the isentropic relativistic Euler system for Chaplygin gas, J. Math. Anal. Appl. 411 (2014), 506-521 (with Gan Yin)
Limits of Riemann solutions to the relativistic Euler systems for Chaplygin gas as pressure vanishes, ABSRT APPL ANAL. 2013 (with Gan Yin)
Semi-hyperbolic patches arising from a transonic shock in simple waves interaction, J. Korean Math. Soc. 50 (2013), 945-957
Radial symmetry of topological solutions in the self-dual Maxwell-Chern-Simons O(3) sigma model, Bull. Korean Math. Soc. 48 (2011), 1111-1117
Existence and asymptotics of topological solutions in the self-dual Maxwell-Chern-Simons O(3) sigma model, J. Differential Equations 250 (2011), 204-222 (with Jongmin Han)
Existence and asymptotics of solutions for the Abelian Chern-Simons system with two Higgs fields and two gauge fields, Nonlinear Analysis TMA 74 (2011), 7426-7436 (with Jongmin Han)
Self-similar solutions for the 2-D Burgers system in infinite subsonic channels, Bull. Korean Math. Soc. 47 (2010), 29-37.
On the Chern-Simons limit for a Maxwell-Chern-Simons model on bounded domains, J. Math. Anal. Appl. 350 (2009), 1-8 (with Jongmin Han)
Semi-hyperbolic patches of solutions of the pressure gradient system, Discrete Contin. Dyn. Syst. A 24 (2009), 1365-1380 (with Yuxi Zheng)
Nonrelativistic limit in the self-dual abelian Chern-Simons model, J. Korean Math. Soc. 44 (2007), 997-1012 (with Jongmin Han)
Two-dimensional transonic flows through a nozzle for the full Euler equations, J. Differential Equations 229 (2006), 92-120 (with Gui-Qiang Chen and Jun Chen)
Transonic flow arising from 2-D Riemann problems, Contemporary Mathematics AMS 371 (2005), 297-313
Classical solutions for the pressure-gradient equations on non-smooth and non-convex domains, J. Math. Anal. Appl. 293 (2004), 541-550 (with Eun Heui Kim)
On singularity of a nonlinear variational sine-Gordon equation, J. Differential Equations 189 (2003), 183-198
A pressure-gradient system on non-smooth domains, Comm. Partial Differential Equations 28 (2003), 199-221