I’m interested in Partial differential equations. Specifically, I study free-boundary problems in fluid dynamics.
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
Z. Hu, C.Luo and Y. Yao. Small Scale Creation for 2D Free Boundary Euler equations with Surface Tension. Preprint, 2023. https://arxiv.org/abs/2309.08137. 17 pp.
C.Luo and K. Zhou. A Generalized Beale-Kato-Majda Breakdown Criterion for the Free-Boundary Problem in Euler Equations with Surface Tension. Preprint, 2023. https://arxiv.org/abs/2302.08125. 31 pp. SIAM Journal on Mathematical Analysis (to appear).
C.Luo. Compressible Water Waves with Vorticity: An Overview. Preprint, 2022. 25 pp.
C.Luo and J. Zhang. Compressible Gravity-Capillary Water Waves with Vorticity: LocalWell-Posedness, Incompressible and Zero-Surface-Tension Limits. Preprint, 2022. https://arxiv.org/abs/2211.03600. 63pp.
C.Luo and H. Yu. Nematic Liquid Crystal Flows with Low Viscosity. Preprint, 2022. 14 pp.
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. LocalWell-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 flowwith 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 Honor 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.