University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
An intrinsic hyperboloid approach for Einstein Klein-Gordon equations
Journal of Differential Geometry issue 1 volume 115 page 27-109 (7 April 2020)
Global solution for massive Maxwell-Klein-Gordon equations
Communications on Pure and Applied Mathematics issue 1 volume 73 page 63-109 (23 August 2019)
A geometric perspective on the method of descent
Communications in Mathematical Physics issue 3 volume 360 page 827–850- (12 May 2018)
A geometric approach for sharp Local well-posedness of quasilinear wave equations
Annals of PDE issue 1 volume 3 page 12- (1 May 2017)
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 by J.D.G
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, 34 pages, joint work with S. Klainerman and S. Yang. Accepted in Oct, 2018 by CPAM.
On the exterior stability of nonlinear wave equations. Preprint 2018, arxiv:1808.02415, 68 pages.
Global solution for Massive Maxwell-Klein-Gordon equations with large Maxwell field, 47 pages, Preprint 2018, joint with A, Fang, and S. Yang. arXiv:1902.08927
Rough solutions of the $3$-D compressible Euler equations. Preprint 2019, arXiv:1911.05038 [math.AP], 110 pages.