The Fuchsian approach to global existence for hyperbolic equations

Florian Beyer, Todd A. Oliynyk, J. Arturo Olvera-Santamaría

备注：: Introduction expanded, references added, and typos fixed. Accepted for publication in Communications in Partial Differential Equations
发表信息：: Comm. Part. Diff. Eqns. 46 (2021), 864-934

英文摘要：

We analyze the Cauchy problem for symmetric hyperbolic equations with a time singularity of Fuchsian type and establish a global existence theory along with decay estimates for evolutions towards the singular time under a small initial data assumption. We then apply this theory to semilinear wave equations near spatial infinity on Minkowski and Schwarzschild spacetimes, and to the relativistic Euler equations with Gowdy symmetry on Kasner spacetimes.

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