Generalized wave operators for a system of nonlinear wave equations in three space dimensions

TL;DR

This paper establishes the global solvability of the final value problem for a spherically symmetric system of nonlinear wave equations with long-range nonlinearity, enabling the construction of generalized wave and scattering operators.

Contribution

It introduces a method to solve the final value problem for nonlinear wave systems with long-range interactions under spherical symmetry, extending scattering theory.

Findings

Global solvability of the final value problem is proven.

Construction of generalized wave operators is achieved.

Long-range scattering operators are developed.

Abstract

This paper is concerned with the final value problem for a system of nonlinear wave equations. The main issue is to solve the problem for the case where the nonlinearity is of a long range type. By assuming that the solution is spherically symmetric, we shall show global solvability of the final value problem around a suitable final state, and hence the generalized wave operator and long range scattering operator can be constructed.