Global Existence for Coupled 3-D Nonlinear Wave and Klein-Gordon Equations with Large Derivatives of Initial Data

TL;DR

This paper proves the global existence of solutions for coupled 3-D wave and Klein-Gordon equations with large initial derivatives, under null conditions and specific assumptions, advancing understanding of nonlinear wave dynamics.

Contribution

It establishes global existence results for coupled wave and Klein-Gordon equations with large derivatives, incorporating null conditions and broad initial data classes.

Findings

Global solutions exist under null conditions.

Large derivative initial data are permissible.

Conditions extend previous small-data results.

Abstract

We consider the Cauchy problem of coupled 3-D wave and Klein-Gordon equations with a quadratic form of nonlinearity. We show global existence under several conditions, including large derivative data for wave equations and the null conditions.