Current Research Projects:
Some of the Previous Research Results:
1. Mathematical theory of shock reflection/diffraction and von Nuemann’s conjectures, including the solution to the von Neumann's sonic conjecture and detachment conjecture for shock reflection-diffraction for potential flow (with M. Feldman).
transonic shock waves, free boundary problems, and nonlinear PDEs of mixed hyperbolic-elliptic
3. Compactness and continuity of nonlinear partial differential equations, including the isentropic Euler equations, compensated compactness, and related problems in nonlinear conservation laws.
theory for hyperbolic conservation laws with stiff relaxation terms (with D. Levermore & T.-P. Liu):
theory and applications of divergence-measure fields and conservation laws,
including the Gauss-Green theorem and normal traces for weakly differentiable
6. Well-posedness theory and large-time asymptotic behabior of solutions for anisotropic degenerate parabolic-hyperbolic equations (with Benoit Perthame):
7. Isometric embedding and weak continuity of the Gauss-Codazzi-Gauss equations
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.
Vanishing Viscosity Solutions of the
Compressible Euler Equations with Spherical Symmetry and Large Initial Data.
This page last modified by Gui-Qiang Chen
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