My research interest focuses on partial differential equations that arise from general relativity (GR) and fluid mechanics. For GR, my current research concerns the formation of black holes, black hole boundaries (e.g. apparent horizon), the stability of black holes and big bang singularities in cosmology. Regarding the field of fluid dynamics, I am interested in the stability problem of typical solutions to incompressible Euler/Navier-Stokes equations.
8. An extension principle for Einstein-Maxwell-charged scalar field system with finite Doppler exponent (with Xinliang An and Haoyang Chen), arXiv:2610.20469 (2026).
7. Stability of Big Bang Singularity for the Einstein-Maxwell-Scalar Field-Vlasov System in the Full Strong Sub-Critical Regime (with Xinliang An and Dawei Shen), arXiv:2507.18585 (2025).
6. On Kerr black hole formation with complete apparent horizon and a new approach toward Penrose inequality (with Xinliang An), arXiv: 2505.11399 (2025).
5. Angular momentum memory effect (with Xinliang An and Dawei Shen), arXiv:2403.11133 (2024).
4. Dynamics of apparent horizon and a null comparison principle (with Xinliang An), Ann. PDE 10(2), 15 (2024).
3. Nonlinear asymptotic stability and transition threshold for 2D Taylor-Couette flows in Sobolev spaces (with Xinliang An and Te Li), Comm. Math. Phys 405.6 (2024): 146.
2. Quantitative blow-up estimates for spacelike singularities in gravitational-collapse cosmological spacetimes (with Xinliang An and Haoyang Chen), Calc. Var. Partial Differ. Equ. 64(3), 75 (2025).
1. Enhanced dissipation and nonlinear asymptotic stability of the Taylor-Couette flow for the 2D Navier-Stokes equations (with Xinliang An and Te Li), arXiv:2112.15357 (2021).
1. Kerr black hole formation and a dynamical approach to the Penrose inequality (with Xinliang An), Séminaire Laurent Schwartz, EDP et applications Institut des hautes études scientifiques, 2025-2026 Expose no IX, 1-18.
Stability of Big Bang Singularity for the Einstein-Maxwell-Scalar Field-Vlasov System in the Full Strong Sub-Critical Regime, Shanghai Institute for Mathematics and Interdisciplinary Sciences, China (08/2026)
On Kerr Black Hole Formation With Complete Apparent Horizon and a New Approach Toward Penrose Inequality, Séminaire Laurent Schwartz, IHES, France (03/2026)
Stability of Big Bang Singularity for the Einstein-Maxwell-Scalar Field-Vlasov System in the Full Strong Sub-Critical Regime, The 2nd Asia-Pacific International Conference on Dispersive Equations (APICDE-II), Macquarie University, Sydney, Australia (02/2026)
Stability of Big Bang Singularity for the Einstein-Maxwell-Scalar Field-Vlasov System in the Full Strong Sub-Critical Regime, Analysis & PDE Seminar, National University of Singapore, Singapore (01/2026)
Stability of Big Bang Singularity for the Einstein-Maxwell-Scalar Field-Vlasov System in the Full Strong Sub-Critical Regime. Comprehensive Mathematics Seminar, School of Mathematical sciences, Fudan University, China (01/2026).
Stability of Big Bang Singularity for the Einstein-Maxwell-Scalar Field-Vlasov System in the Full Strong Sub-Critical Regime. General Relativity seminar, Chinese Academy of Sciences (09/2025).
On Kerr Black Hole Formation with Complete Apparent Horizon and a New Approach Toward Penrose Inequality: Part II. Mathematical GR and Hyperbolic PDE Seminar, Columbia University (online) (06/2025).
On Kerr black hole formation and a new approach toward Penrose inequality. The Joint FDU-NUS-ZJU PhD Forum in Mathematics, National University of Singapore, Singapore (06/2025).
On Kerr Black Hole Formation with Complete Apparent Horizon and a New Approach Toward Penrose Inequality: Part II. Seminar on Black Hole Formation, Yau Mathematical Sciences Center, Tsinghua University, China (05/2025).
On Kerr black hole formation with complete apparent horizon and a new approach toward Penrose inequality. The 9th NUS Graduate Symposium in Mathematics, National University of Singapore, Singapore (05/2025).
Tutorial lectures: 1. Local well-posedness of Einstein vacuum equations; 2. Spacetime decomposition and double null formalism. Singularities in Fluids and General Relativity, IMS (Institute for Mathematical Sciences), National University of Singapore, Singapore (12/2024).
Angular Momentum Memory Effect. IPS (Institute of Physics Singapore) Meeting 2024, Nanyang Technological University, Singapore (10/2024).
Dynamics of Apparent Horizon, Null Comparison Principle and Angular Momentum Memory Effect. International Conference on Ricci Curvature and Geometric Analysis (ICRG2024), Xi'an Jiaotong University, China (08/2024).
Dynamics of Apparent Horizon and a Null Comparison Principle. Comprehensive Mathematics Seminar, School of Mathematical sciences, Fudan University, China (08/2024).
Dynamics of Apparent Horizon and a Null Comparison Principle. The 21st International Congress of Mathematical Physics (ICMP), Strasbourg, France (07/2024).
Angular Momentum Memory Effect. The 27th Capra Meeting on Radiation Reaction in General Relativity, National University of Singapore, Singapore (06/2024).
Angular Momentum Memory Effect. Analysis & PDE Seminar, National University of Singapore (03/2024).
Nonlinear asymptotic stability and transition threshold for 2D Taylor-Couette flows in Sobolev spaces. The 12th Symposium of SIAM Student Chapter at NUS, National University of Singapore, Singapore (05/2023).
Workshop: PDE perspectives in gravitational theory, Edinburgh, United Kingdom (09/2026)
Conference: Randomness, Analysis and PDEs, Conference for Nicolas Burq's 60th birthday, Pisa, Italy (07/2026)
Summer school: Mathematics of General Relativity and Fluids, Forth, Greece (07-08/2024).
Summer school: New Trends in Mathematical Fluid Dynamics, Université Grenoble Alpes, France (06/2023).