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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)
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
TWO-DIMENSIONAL STEADY SUPERSONIC EXOTHERMICALLY REACTING EULER FLOW PAST LIPSCHITZ BENDING WALLS
SIAM JOURNAL ON MATHEMATICAL ANALYSIS issue 2 volume 49 page 818-873 (2017) Full text available
TRANSONIC FLOWS WITH SHOCKS PAST CURVED WEDGES FOR THE FULL EULER EQUATIONS
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS issue 8 volume 36 page 4179-4211 (August 2016) Full text available
Gui-Qiang G. Chen's main research areas lie in nonlinear 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, 2017 (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