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Polyhomogeneous solutions of wave equations in the radiation regime

Piotr T. Chruściel;  Olivier Lengard — 2000

Journées équations aux dérivées partielles

While the physical properties of the gravitational field in the radiation regime are reasonably well understood, several mathematical questions remain unanswered. The question here is that of existence and properties of gravitational fields with asymptotic behavior compatible with existence of gravitational radiation. A framework to study those questions has been proposed by R. Penrose (R. Penrose, “Zero rest-mass fields including gravitation”, Proc. Roy. Soc. London A284 (1965), 159-203), and developed...

Radiation fields

Piotr T. Chruściel;  Olivier Lengard — 2005

Bulletin de la Société Mathématique de France

We study the “hyperboloidal Cauchy problem” for linear and semi-linear wave equations on Minkowski space-time, with initial data in weighted Sobolev spaces allowing singular behavior at the boundary, or with polyhomogeneous initial data. Specifically, we consider nonlinear symmetric hyperbolic systems of a form which includes scalar fields with a λ φ p nonlinearity, as well as wave maps, with initial data given on a hyperboloid; several of the results proved apply to general space-times admitting conformal...

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