On the Cauchy problem for the Fadaray tensor on globally hyperbolic manifolds with timelike boundary

Nicolas Ginoux; Nicol\'o Drago; Simone Murro

On the Cauchy problem for the Fadaray tensor on globally hyperbolic manifolds with timelike boundary

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arxiv 2306.06896 v2 pith:QNI3HIOJ submitted 2023-06-12 math.AP math-phmath.DGmath.MP

Nicoló Drago , Nicolas Ginoux , Simone Murro This is my paper · ORCID

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keywords boundarycauchygloballyhyperbolicmanifoldsproblemtensortimelike

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abstract

We study the well-posedness of the Cauchy problem for the Faraday tensor on globally hyperbolic manifolds with timelike boundary. The existence of Green operators for the operator $\mathrm{d}+\delta$ and a suitable pre-symplectic structure on the space of solutions are discussed.

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The Cauchy Problem for Symmetric Hyperbolic Systems with Nonlocal Potentials
math.AP 2025-07 conditional novelty 7.0 of 10

Under smallness and decay conditions on nonlocal potentials, symmetric hyperbolic systems on curved spacetimes admit strong solutions to the Cauchy problem, with a sharp threshold beyond which solutions fail.

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