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Image of Prof. Qian Wang

Prof. Qian Wang

PhD
Status
Academic Faculty

Associate Professor

Contact form
CV
+44 1865 615122
Research groups
  • Oxford Centre for Nonlinear PDE

Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Recent publications
Rough solutions of the 3-D compressible Euler equations
Wang, Q Annals of Mathematics volume 195 issue 2 509-654 (28 Feb 2022)
On the exterior stability of nonlinear wave equations
Wang, Q Annals of PDE volume 6 issue 2 (09 Jul 2020)
An intrinsic hyperboloid approach for Einstein Klein-Gordon equations
Wang, Q Journal of Differential Geometry volume 115 issue 1 27-109 (07 Apr 2020)
Global solution for massive Maxwell-Klein-Gordon equations
Klainerman, S Wang, Q Yang, S Communications on Pure and Applied Mathematics volume 73 issue 1 63-109 (23 Aug 2019)
A geometric perspective on the method of descent
Wang, Q Communications in Mathematical Physics volume 360 issue 3 827-850 (12 May 2018)
Research interests

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.

Teaching

TCC course: Nonlinear wave equations

Friday 1-3 pm

18/Jan/2013--08/March/2013 Lecture 1 (.pdf)  

 

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, 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.

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