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A Geometric Approach for Sharp Local Well-Posedness of Quasilinear Wave Equations
Annals of PDE issue 1 volume 3 (30 June 2017)
On Ricci coefficients of null hypersurfaces with time foliation in Einstein vacuum space-time: part I
Calculus of Variations and Partial Differential Equations issue 3-4 volume 46 page 461-503 (7 March 2013)
Rough solutions of Einstein vacuum equations in CMCSH gauges
Communications in Mathematical Physics (2013) Full text available
My research interest includes Partial differential equations and analysis with a focus on the study of nonlinear wave equations. I have
been working on Cauchy problem for quasilinear wave equations, including breakdown criterion for Einstein vacuum equations, local well-posedness of solution for very rough data and global nonlinear stability of Minkowski space with cerntain matter fields.
Major / recent publications:
Causal geometry of Einstein vacuum spacetimes.Ph.D thesis (.dvi), Princeton University 2006,
On the geometry of null cones in Einstein Vacuum Spacetimes, Ann.Inst. H. Poincar\`e Anal. Non Lin\'eaire, 26 (2009), no. 1,285--328.
Improved breakdown criterion for Einstein vacuum equation in CMC gauge , Comm. Pure Appl. Math, Vol. 65, Issue 1, 0021-0076 (2012)
On Ricci coefficients of null hypersurfaces with time foliation in Einstein vacuum space-time: Part I , Calculus of Variations and Partial Differential Equations, March 2013, Volume 46, Issue 3-4, pp 461-503
On Ricci coefficients of null hypersurfaces with time foliation inEinstein vacuum space-time: Part II (.pdf), (see arXiv:1006.5963)
Rough solutions of Einstein vacuum equations in CMCSH gauges (arXiv:1201.0049) Communications in Mathematical Physics}, 328 (2014), Issue 3, 1275--1340
Causal geometry of rough Einstein CMCSH spacetime, Journal of Hyperbolic Differential Equations, 11 (2014), No. 3, 563--601.
A geometric approach for sharp Local well-posedness of quasilinear wave equations, arXiv:1408.3780 [math.AP], preprint, 2014. Annals of PDE, 3 (2017), no. 1, 108 pages.
An intrinsic hyperboloid approach for Einstein Klein-Gordon equations, arXiv:1607.01466[math.AP], preprint 2016. Accepted in July 2018
Global existence for the Einstein equations with massive scalar fields. Preprint in preparation
A geometric perspective of the method of descent. arXiv:1703.06458, Communications in Mathematical Physics 360(3):827-850, Jun 2018.
Global solution for massive Maxwell-Klein-Gordon equations arXiv: 1801.10380, preprint 2017, joint work with S. Klainerman and S. Yang. Accepted in Oct, 2018.
On the exterior stability of nonlinear wave equations. Preprint 2018, arxiv:1808.02415
Global solution for Massive Maxwell-Klein-Gordon equations with large Maxwell field, 47 pages, Preprint 2018, joint with A, Fang, and S. Yang.