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Pré-Publication, Document De Travail Année : 2016

Boundedness of the total energy of relativistic membranes evolving in a curved spacetime

Résumé

We establish a global existence theory for the equation governing the evolution of a relativistic membrane in a (possibly curved) Lorentzian manifold, when the spacetime metric is a perturbation of the Minkowski metric. Relying on the Hyperboloidal Foliation Method introduced by LeFloch and Ma in 2014, we revisit a theorem established earlier by Lindblad (who treated membranes in the flat Minkowski spacetime) and we provide a simpler proof of existence, which is also valid in a curved spacetime and, most importantly, leads to the important property that the total energy of the membrane is globally bounded in time.
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Dates et versions

hal-01423464 , version 1 (29-12-2016)

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  • HAL Id : hal-01423464 , version 1

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Philippe G Lefloch, Changhua Wei. Boundedness of the total energy of relativistic membranes evolving in a curved spacetime. 2016. ⟨hal-01423464⟩
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