GLOBAL EXISTENCE FOR A CLASS OF SYSTEMS OF NONLINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS

摘要

Consider a system of nonlinear wave equations ((partial deriv)_t~2-c_i~2Δ_x)u_i = F_i(u, partial deriv u, (partial deriv) _x partial deriv u in (0, ∞) x R~3 for i = 1, ··· , m, where Fi (i = 1, ··· , m) are smooth functions of degree 2 near the origin of their arguments, and u = (u_1 ,···, u_m), while partial deriv u and (partial deriv)_x partial deriv u represent the first and second derivatives of u, respectively. In this paper, the author presents a new class of nonlinearity for which the global existence of small solutions is ensured.