Abstract
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 toward 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.
Original language | English |
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Number of pages | 71 |
Journal | Communications in Partial Differential Equations |
DOIs | |
Publication status | Accepted/In press - 2020 |
Keywords
- Decay estimates
- Fuchsian equations
- global existence
- non-linear wave equations
- null condition
- system of hyperbolic equations