Partial Differential Equations with Free Surface Boundary, Fluid Dynamics, Magnetohydrodynamic (MHD), General Relativity.

2020-, Assistant Professor, Department of Mathematics, Chinese University of Hong Kong

2017-2020, NTT Assistant Professor, Department of Mathematics, Vanderbilt University

2017 Ph.D in Mathematics, Johns Hopkins University

2011 BA in mathematics with highest honor, University of Rochester

C.Luo and J. Zhang. Compressible Gravity-Capillary Water Waves with Vorticity: Local Well-Posedness, Incompressible and Zero-Surface-Tension Limits. Preprint, 2022. https://arxiv.org/abs/2211.03600. 61pp.

C.Luo and H. Yu. Nematic Liquid Crystal Flows with Low Viscosity. Preprint, 2022. 14pp.

X. Gu, C. Luo and J. Zhang. Zero Surface Tension Limit of the Free-Boundary Problem in Incompressible Magnetohydrodynamics. Nonlinearity (2022), 35, no.12, 6349.

X. Gu, C. Luo and J. Zhang. Local Well-posedness of the Free-Boundary Incompressible Magnetohydrodynamics with Surface Tension. Preprint, 2021. https://arxiv.org/abs/2105.00596 64pp.

C. Luo and J. Zhang. Local Well-Posedness for the Motion of a Compressible Gravity Water Wave with Vorticity. Journal of Differential Equations (2022) 332: 333-403.

M. M. Disconzi, C. Luo, G. Mazzone, J. Speck. Rough sound waves in 3D compressible Euler flow with vorticity. Selecta Mathematica 28, no. 2 (2022): 1-153.

C. Luo and J. Zhang. A priori estimate for the incompressible free boundary magnetohydrodynamics equations with surface tension. SIAM Journal on Mathematical Analysis, 53(2), 2595-2630 (2021).

M. M. Disconzi and C. Luo. On the incompressible limit for the free boundary compressible Euler equations with surface tension in the case of a liquid. Arch. Ration. Mech. Anal. 237, 829-897 (2020).

C. Luo and J. Zhang. A regularity result for the incompressible megnetohydrodynamics equations with free surface boundary. Nonlinearity (2020), 33, no.4, 1499.

D. Ginsberg, H. Lindblad and C. Luo. Local well-posedness for the motion of a compressible, self-gravitating liquid with free surface boundary. Arch. Ration. Mech. Anal. 236, 603-733 (2020).

C. Luo. On the motion of a compressible gravity water wave with vorticity. Ann. PDE, 4, no.2, (2018), 1-71.

H. Lindblad and C. Luo. A priori estimate for the compressible Euler equations for a liquid with free surface boundary and the incompressible limit. Comm. Pure Appl. Math, 71, no.7, (2018), 1273-1333.

C. Luo. On the motion of the free surface of a compressible liquid. Ph.D. Thesis (2017).

C. Luo. Constructive Proofs for Malgrange-Ehrenpreis Theorem. Undergraduate Honour Thesis (2011).

01/2023-12/2026, Hong Kong RGC General Research Fund (GRF), Project No. CUHK-14302922.

07/2022-06/2024, Collaborative Research Impact Matching Scheme (CRIMS), Project No. 4620031. Co-PIs: Yong Yu (Mathematics), Hua-bai Li (Physics).

07/2021-06/2024, Hong Kong RGC Early Career Scheme (ECS), Project No. CUHK-24304621.