This set of lecture notes was written for a Nachdiplom-Vorlesungen course given at the
Forschungsinstitut fUr Mathematik (FIM), ETH Zurich, during the Fall Semester 2000. I would …

This book gives a general presentation of the mathematical and numerical connections
kinetic theory and conservation laws based on several earlier works with PL Lions and E …

The method of compensated compactness as a technique for studying hyperbolic
conservation laws is of fundamental importance in many branches of applied mathematics …

We establish the vanishing viscosity limit of the Navier‐Stokes equations to the isentropic
Euler equations for one‐dimensional compressible fluid flow. For the Navier‐Stokes …

Some recent developments in the study of the Cauchy problem for the Euler equations for
compressible fluids are reviewed. The local and global well-posedness for smooth solutions …

Abstract The Euler-Maxwell equations as a hydrodynamic model of charge transport of
semiconductors in an electromagnetic field are studied. The global approximate solutions to …

A compensated compactness framework is established for sonic-subsonic approximate
solutions to the two-dimensional Euler equations for steady irrotational flows that may …

We study the hyperbolic system of Euler equations for an isothermal, compressible fluid. The
strong convergence theorem of approximate solutions is proved by the theory of …

The Riemann problem for one dimensional generalized Chaplygin gas dynamics is
considered. Its two characteristic fields are genuinely nonlinear, but the nonclassical …

This is the first of a series of papers devoted to the initial value problem for the one‐
dimensional Euler system of compressible fluids and augmented versions containing higher …