Prof. Qian Wang
Associate Professor
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
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.
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, accepted by Annals of PDE
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, accepted by Annals of PDE.
Rough solutions of the $3$-D compressible Euler equations. Preprint 2019, arXiv:1911.05038 [math.AP], 110 pages, accepted by Annals of Mathematics, Oct 2021.
On the global rarefaction waves for $3$-D compressible Euler equations. Preprint 2023. 200 pages.