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The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures
ISBN-13: 9780691160559 (16 January 2018) Full text available
Differential Geometry and Continuum Mechanics
Springer Proceedings in Mathematics and Statistics volume 137 page VII-VII (1 January 2015)
Hyperbolic Conservation Laws and Related Analysis with Applications
ISBN-13: 9783642390067 (7 February 2014)
Nonlinear Conservation Laws and Applications
ISBN-13: 9781441995537 (31 March 2011)
Stochastic Analysis and Partial Differential Equations
ISBN-13: 9780821840597 (May 2007)
Nonlinear Partial Differential Equations
ISBN-13: 9780821811962 (1999)
Global Weak Rigidity of the Gauss–Codazzi–Ricci Equations and Isometric Immersions of Riemannian Manifolds with Lower Regularity
Journal of Geometric Analysis page 1-51 (18 August 2017)
Stability of transonic shocks in steady supersonic flow past multidimensional wedges
ADVANCES IN MATHEMATICS volume 314 page 493-539 (9 July 2017) Full text available
Vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for compressible fluid flow
Communications on Pure and Applied Mathematics issue 11 volume 63 page 1469-1504 (1 November 2010)
Isometric immersions and compensated compactness
Communications in Mathematical Physics issue 2 volume 294 page 411-437 (1 January 2010)
Global solutions of shock reflection by large-angle wedges for potential flow
Annals of Mathematics issue 2 volume 171 page 1067-1182 (2010)
Large-time behavior of periodic entropy solutions to anisotropic degenerate parabolic-hyperbolic equations
Proceedings of the American Mathematical Society issue 9 volume 137 page 3003-3011 (1 September 2009)
Vanishing Viscosity Approach to the Compressible Euler Equations for Transonic Nozzle and Spherically Symmetric Flows
Archive for Rational Mechanics and Analysis page 1-41 (3 April 2018)
Stability and asymptotic behavior of transonic flows past wedges for the full Euler equations
INTERFACES AND FREE BOUNDARIES issue 4 volume 19 page 591-626 (15 February 2018) Full text available
Fluids, geometry, and the onset of Navier–Stokes turbulence in three space dimensions
Physica D: Nonlinear Phenomena (31 October 2017)
Fluids, Elasticity, Geometry, and the Existence of Wrinkled Solutions
Archive for Rational Mechanics and Analysis page 1-52 (8 August 2017)
Global existence and regularity of solutions for active liquid crystals
Journal of Differential Equations issue 1 volume 263 page 202-239 (5 July 2017) Full text available
Supersonic flow onto solid wedges, multidimensional shock waves and free boundary problems
Science China Mathematics page 1-18 (6 May 2017) Full text available
Gui-Qiang G. Chen's main research areas lie in partial differential equations (PDEs), nonlinear analysis, and their connections/applications to mechanics, geometry, other areas of mathematics and the other sciences. His recent research interests include nonlinear hyperbolic conservation laws, shock wave theory, PDEs of mixed type, free boundary problems, geometric problems, and other related nonlinear problems. His research interests also include measure-theoretical analysis, weak convergence methods, stochastic PDEs, statistical physics, and numerical analysis.
Major / Recent Publications:
- The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures, Research Monograph (Original Research), 832 pages, Princeton Math Series in Annals of Mathematics Studies, 197, Princeton University Press, January 2018 (with Mikhail Feldman).
- Free Boundary Problems and Related Topics, Theme Issue 2050, Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences, Vol. 373, September 13, 2015 (with Henrik Shahgholian & Juan Luis Vázquez).
- Differential Geometry and Continuum Mechanics, Springer: Cham-Heidelberg-New York, 2015 (with Michael Grinfeld & Robin J. Knops).
- Hyperbolic Conservation Laws and Related Analysis with Applications, Springer-Verlag: Berlin-Heidelberg, 2014 (with Helge Holden & Kenneth. H. Karlsen).
- Entropy and Convexity for Nonlinear Partial Differential Equations, Theme Issue 2005, Philosophical Transactions of the Royal Society A: Mathemaitcal, Physical & Engineering Sciences, Vol. 371, December 28, 2013 (with John M. Ball).
- Nonlinear Conservation Laws and Applications, Springer-Verlag: New York, 2011 (with Alberto Bressan, Marta Lewicka & Dehua Wang).
Supervised DPhil/PhD Thesis Research Topics:
Some of them can be found on the Mathematics Genealogy Project