Well-posedness of inhomogeneous nonlinear wave equations in $\mathbb{R}^3$

TL;DR

This paper proves local and global well-posedness for inhomogeneous nonlinear wave equations in three-dimensional space using Strichartz estimates and contraction mapping, extending previous results in the energy-subcritical regime.

Contribution

It establishes new well-posedness results for inhomogeneous nonlinear wave equations in specific Sobolev spaces, improving upon prior work.

Findings

Proves local and global well-posedness in specified function spaces.

Extends previous results to more general nonlinear wave equations.

Operates within the energy-subcritical regime.

Abstract

This paper is devoted to the well-posedness of the inhomogeneous nonlinear wave equations. By combining Strichartz estimates with the contraction mapping principle, we establish local and global well-posedness in the function spaces $\dot{H}^1(\mathbb{R}^3)\times L^2(\mathbb{R}^3)$ and $\dot{H}^{s+1}(\mathbb{R}^3)\times \dot{H}^{s}(\mathbb{R}^3)$. The analysis is carried out in the energy-subcritical regime. As a consequence, our results extend and improve upon previous results in the literature for general nonlinear wave equations.