Compressible Euler-Maxwell Equations

By: Gui-Qiang Chen, Joseph W. Jerome, and Dehua Wang

The Euler-Maxwell equations as a hydrodynamic model of charge transport of semiconductors in an electromagnetic field are studied. The global approximate solutions to the initial-boundary value problem are constructed by the fractional Godunov scheme. The uniform bound and energy space compactness are proved. The approximate solutions are shown convergent by weak convergence methods. Then, with some new estimates due to the presence of electromagnetic fields, the existence of a global weak solution to the initial-boundary value problem is established for arbitrarily large initial data in the space of essentially bounded functions.
This paper appears in Transport Theory and Statistical Physics, vol. 29 (2000), pages 311--331. It can be viewed in the following format: