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∞.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics