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

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.

34pages

References in corpus (2)

• Improved decay for solutions to the linear wave equation on a Schwarzschild black hole
• The wave equation on Schwarzschild-de Sitter spacetimes

Cited by in corpus (1)

• Integral transform approach to solving Klein-Gordon equation with variable coefficients