Abstract
This paper is concerned with the classical solution to the Cauchy problem of relativistic Burger’s equation evolving on exterior Schwarzschild-(anti-)de Sitter (for convenience, we use SdS to denote Schwarzschild-de Sitter and SAdS to denote Schwarzschild-anti-de Sitter, respectively) spacetimes, which are spherically symmetric black hole solutions to the Einstein vacuum field equations with cosmological constant. We aim at giving a classification of the initial data under which the classical solution can exist globally or blow up in finite time on Schwarzschild-(anti-)de Sitter spacetimes. We also discuss clearly the effect of the cosmological constant and the universe mass to the stabilization of the fluids.
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