Compressible Euler-Maxwell Equations

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 H−1 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 L∞. Acknowledgements: The research of the first author is supported by Office of Naval Research grant N00014-91-J-1384, by National Science Foundation grant DMS-9623203, and by an Alfred P. Sloan fellowship. The research of the second author is supported by National Science Foundation grants DMS-9424464 and DMS-9704458.