Global well-posedness of first-order mean field games and master equations with nonlinear dynamics
ESAIM: Control, Optimisation and Calculus of Variations, 32 (2026), No. 59.
Publications
Following are some published papers, as well as preprints. (The papers on arXiv are NOT their final versions.)
A Control Theoretical Approach to Mean Field Games. Part II: Global Well-Posedness of Master Equations
Applied Mathematics and Optimization, 93 (2026), Paper No. 45.
A theory of first order mean field type control problems and their equations
Journal of the European Mathematical Society (2026).
A Control Theoretical Approach to Mean Field Games: Part I—Global Equilibrium Solution
Applied Mathematics and Optimization, 92 (2025), Paper No. 44.
Viscosity solution for optimal liquidation problems with randomly-terminated horizon
Finance Res. Lett., 61 (2024), 105043.
On the characterization, existence and uniqueness of steady solutions to the hydrostatic Euler equations in a nozzle
Arch. Ration. Mech. Anal., 248 (2024), Paper No. 116.
Asymptotic behavior of conservative solutions to the Hunter-Saxton equation
SIAM J. Math. Anal., 55 (2023), No. 5, 5483-5525.
Stability of peakons of the Camassa-Holm equation beyond wave breaking
J. Math. Phys., 63 (2022), 121503.
Magnetic confinement for the 2D axisymmetric relativistic Vlasov-Maxwell system in an annulus
Kinetic & Related Models, 15 (2022), No. 4, 569-604.
Regularity structure of conservative solutions to the Hunter-Saxton equation
SIAM J. Math. Anal., 54 (2022), No. 1, 423-452.
The inverse first passage time problem for killed Brownian motion
Ann. Appl. Probab., 30 (2020), No. 3, 1251-1275.
Asymptotic harvesting of populations in random environments
J. Math. Biol., 78 (2019), 293-329.
A probabilistic proof for Fourier inversion formula
Statistics & Probability Letters, 141 (2018), 135-142.
Axisymmetric flow of ideal fluid moving in a narrow domain: a study of the axisymmetric hydrostatic Euler equations
J. Differential Equations, 260 (2016), No. 5, 4619-4656.
Local-in-time existence and uniqueness of solutions to the Prandtl equations by energy methods
Comm. Pure Appl. Math., 68 (2015), 1683-1741.
Blowup of solutions of the hydrostatic Euler equations
Proc. Amer. Math. Soc., 143 (2015), 1119-1125.
Long time solutions for a Burgers-Hilbert equation via a modified energy method
Proc. Amer. Math. Soc., 143 (2015), 3407-3412.
On the local well-posedness of the Prandtl and hydrostatic Euler equations with multiple monotonicity regions
SIAM J. Math. Anal., 46 (2014), No. 6, 3865-3890.
On the $H^s$ theory of hydrostatic Euler equations
Arch. Ration. Mech. Anal., 204 (2012), No. 1, 231-271.