The Two-Dimensional Riemann Problem in Gas Dynamics establishes the rigorous mathematical theory of delta-shocks and Mach reflection-like patterns for zero-pressure gas dynamics, clarifies the boundaries of interaction of elementary waves, demonstrates the interesting spatial interaction of slip lines, and proposes a series of open problems.

Jiequan Li (Author) , Tong. Zhang (Author) , Shuli Yang (Academia Sinica, Beijing, China)

Geometry of Characteristics and Discontinuities, Riemann Solution Geometry of Conservation Laws, Scalar Conservation Laws, One-Dimensional Scalar Conservation Laws, The Generalized Characteristic Analysis Method, The Four-Wave Riemann Problem, Mach-Reflection-Like Configuration of Solutions, Zero-Pressure Gas Dynamics, Characteristics and Bounded Discontinuities, Simultaneous Occurrence of Two Blowup Mechanisms, Delta-Shocks, Generalized Rankine-Hugoniot Relations and Entropy Conditions, The One-Dimensional Riemann Problem, The Two-Dimensional Riemann Problem, Riemann Solutions as the Limits of Solutions to Self-Similar Viscous Systems, Pressure-Gradient Equations of the Euler System, The Pme-Dimensional Riemann Problem, Characteristics, Discontinuities, Elementary Waves, and Classifications, The Existence of Solutions to a Transonic Pressure-Gradient Equation in an Elliptic Region with Degenerate Datum, The Two-Dimensional Riemann Problem and Numerical Solutions, The Compressible Euler Equations, The Concepts of Characteristics and Discontinuities, Planar Elementary Waves and Classification, PSI Approach to Irrotational Isentropic Flow, Analysis of Riemann Solutions and Numerical Results, Two-Dimensional Riemann Solutions with Axisymmetry