My research interests lie in the analysis of hyperbolic partial differential equations with physical and geometric background, as well as free boundary problems arising in inviscid fluid.
Publications:
(With D. Christodoulou) Compressible Flow and Euler's Equations, (monograph, 602 pp.), Surveys in Modern Mathematics Volume 9, International Press (ISBN 9781571462978), 2014.
(With P. Yu) On the formation of shocks for quasilinear wave equations, Inventiones Mathematicae, 207 (2017), no.2, 697-831.
(With L. Bieri and S. Shahshahani) Asymptotic properties of solutions of the Maxwell Klein Gordon equation with small data, Communications in Analysis and Geometry, Vol. 25, No. 1 (2017), pp. 25-96.
(With L. Bieri, S. Shahshahani and S.Wu) On the motion of a self-gravitating incompressible fluid with free boundary, Communications in Mathematical Physics, 355(1): 161-243, 2017.
(With L. Pei and P. Yu) On classical global solutions of nonlinear wave equations with large data,
International Mathematics Research Notices, Volume 2019, Issue 19, 5859-5913, 2019.
On the formation of shocks for quasilinear wave equations with weak intensity pulse, Annals of PDE (2018) 4:10.
On large global-in-time-solutions to energy-supercritical nonlinear wave equation, AMS Contemporary Mathematics, Volume 725, 2019.
(With J. Krieger) On stability of blow up solutions for the critical co-rotational Wave Maps problem, Duke Mathematical Journal, Volume 169, Number 3 (2020), 435-532.
(With S. Shahshahani) On tidal energy in Newtonian two-body motion, Cambridge Journal of Mathematics, Volume 7, no. 4, 469-585, 2019.
(With S. Shahshahani and S. Wu) Well-posedness for Free Boundary Hard Phase Fluids with Minkowski Background and their Newtonian limit, Cambridge Journal of Mathematics, Volume 9, no. 2, 269-350, 2021.
(With L. Zhang) On tidal energy in Newtonian two-body motion with infinite initial separation, Pure and Applied Mathematics Quarterly, Volume 20 (2024), no. 4, 1973-2007.
(With S. Shahshahani) Well-posedness for the free boundary hard phase model in general relativity, Advances in Mathematics, Volume 443 (2024), Paper No. 109614, 66pp.
(With Z. Hao) On nonlinear instability of liquid Lane-Emden stars
Calculus of Variations and Partial Differential Equations, Volume 63, article number 157 (2024).
(With Z. Hao) On stability analysis for steady states of the free boundary hard phase model in general relativity SIAM Journal on Mathematical Analysis, Vol. 57, Iss. 5 (2025).
Preprints:
(With J. Krieger and W. Schlag) A stability theory beyond the co-rotational setting for critical Wave Maps blow up
(With Z. Hao and W. Huo) Well-posedness for the free boundary barotropic fluid model in general relativity
(With S. Yang and P. Yu) On the motion of charged particles in constant electromagnetic field: the parallel case
Expository papers:
(With L. Bieri, S. Shahshahani and S. Wu) On the motion of a self-gravitating incompressible fluid with free boundary and constant vorticity: An appendix.
A Note on Semi-Linear Wave Equations