GLOBAL EXISTENCE AND ASYMPTOTIC-BEHAVIOR OF SOLUTIONS FOR THE MAXWELL-SCHRODINGER EQUATIONS IN 3 SPACE DIMENSIONS

In this paper we study the global existence and asymptotic behavior of solutions for the Maxwell-Schrodinger equations under the Coulomb gauge condition in three space dimensions with the final states given at t = + infinity. This leads to the construction of the modified wave operator for certain scattered data. It is also shown that for the initial data in the range of the modified wave operator, the initial value problem of the Maxwell-Schrodinger equations has the global solutions in time.