Lifespan of smooth solutions for timelike extremal surface equation in de Sitter spacetime

TL;DR

This paper investigates the lifespan of smooth solutions to the timelike extremal surface equation in de Sitter spacetime, providing lower bounds under small initial data assumptions using weighted energy estimates.

Contribution

It offers new lower bounds on the lifespan of solutions for the generalized timelike extremal surface equation in de Sitter spacetime.

Findings

Established lower bounds for solution lifespan.

Applied weighted energy estimates to analyze solutions.

Focused on small initial data with compact support.

Abstract

In this paper, we study the generalized timelike extremal surface equation in the de Sitter spacetime, which plays an important role in both mathematics and physics. Under the assumption of small initial data with compact support, we investigate the lower bound of lifespan of smooth solutions by weighted energy estimates.