Life-span of classical solutions to hyperbolic geometric flow in two space variables with slow decay initial data

TL;DR

This paper studies how long classical solutions to a hyperbolic geometric flow persist in two spatial dimensions when starting from initial data that decay slowly, providing new estimates and lower bounds for their lifespan.

Contribution

It introduces novel estimates for linear wave equations in two variables and establishes a lower bound for the lifespan of solutions to the hyperbolic geometric flow with flat initial surfaces.

Findings

Derived new estimates for linear wave equations in two dimensions.

Established a lower bound for the lifespan of solutions.

Applied results to hyperbolic geometric flow with asymptotic flat initial data.

Abstract

In this paper we investigate the life-span of classical solutions to the hyperbolic geometric flow in two space variables with slow decay initial data. By establishing some new estimates on the solutions of linear wave equations in two space variables, we give a lower bound of the life-span of classical solutions to the hyperbolic geometric flow with asymptotic flat initial Riemann surfaces.