Gui-Qiang G. Chen

Current Research Projects:

   --Under Construction


Some of  the Previous Research Results:


1.     Mathematical theory of shock reflection/diffraction and von Nuemann’s conjectures, including the solution to the sonic conjecture and detachment conjecture for shock reflection-diffraction for potential flow (with Mikhail Feldman).


2.     Multidimensional transonic shock waves, free boundary problems, and nonlinear PDEs of mixed hyperbolic-elliptic type.

3.     Compactness and continuity of nonlinear partial differential equations, including the isentropic Euler equations, compensated compactness, and related problems in nonlinear conservation laws.


4.     Relaxation theory via entropy for hyperbolic conservation laws with stiff relaxation terms (with David Levermore & Tai-Ping Liu).

5.     Mathematical theory of divergence-measure fields and their underlying connections with and applications to nonlinear conservation laws, including the

new notions of normal traces, product rules, and Gauss-Green formulas for divergence-measure fields over general open domains.

6.     Well-posedness theory and large-time asymptotic behavior of solutions for anisotropic degenerate parabolic-hyperbolic equations (with Benoit Perthame):


7.     Isometric embedding and weak continuity of the Gauss-Codazzi-Gauss equations; connections with the Euler equations and related PDEs in continuum mechanics (fluid dynamics, elasticity, and materials science).


8.     Theoretical analysis of numerical methods, including the first convergence proof of the Lax-Friedrichs scheme and Godunov scheme for the system of isentropic Euler equations.


9.     Vanishing viscosity solutions of the compressible Euler equations with spherical symmetry and large initial data.



--Under  Construction

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