Quasilinear waves and trapping: Kerr-de Sitter space

Peter Hintz[1]; András Vasy[1]

  • [1] Department of Mathematics Stanford University CA 94305-2125, USA

Journées Équations aux dérivées partielles (2014)

  • Volume: 21, Issue: 6, page 1-15
  • ISSN: 0752-0360

Abstract

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In these notes, we will describe recent work on globally solving quasilinear wave equations in the presence of trapped rays, on Kerr-de Sitter space, and obtaining the asymptotic behavior of solutions. For the associated linear problem without trapping, one would consider a global, non-elliptic, Fredholm framework; in the presence of trapping the same framework is available for spaces of growing functions only. In order to solve the quasilinear problem we thus combine these frameworks with the normally hyperbolic trapping results of Dyatlov and a Nash-Moser iteration scheme.

How to cite

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Hintz, Peter, and Vasy, András. "Quasilinear waves and trapping: Kerr-de Sitter space." Journées Équations aux dérivées partielles 21.6 (2014): 1-15. <http://eudml.org/doc/275534>.

@article{Hintz2014,
abstract = {In these notes, we will describe recent work on globally solving quasilinear wave equations in the presence of trapped rays, on Kerr-de Sitter space, and obtaining the asymptotic behavior of solutions. For the associated linear problem without trapping, one would consider a global, non-elliptic, Fredholm framework; in the presence of trapping the same framework is available for spaces of growing functions only. In order to solve the quasilinear problem we thus combine these frameworks with the normally hyperbolic trapping results of Dyatlov and a Nash-Moser iteration scheme.},
affiliation = {Department of Mathematics Stanford University CA 94305-2125, USA; Department of Mathematics Stanford University CA 94305-2125, USA},
author = {Hintz, Peter, Vasy, András},
journal = {Journées Équations aux dérivées partielles},
keywords = {semiclassical resolvent estimates; trapping; normal hyperbolicity; propagation of singularities; b-calculus},
language = {eng},
number = {6},
pages = {1-15},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Quasilinear waves and trapping: Kerr-de Sitter space},
url = {http://eudml.org/doc/275534},
volume = {21},
year = {2014},
}

TY - JOUR
AU - Hintz, Peter
AU - Vasy, András
TI - Quasilinear waves and trapping: Kerr-de Sitter space
JO - Journées Équations aux dérivées partielles
PY - 2014
PB - Groupement de recherche 2434 du CNRS
VL - 21
IS - 6
SP - 1
EP - 15
AB - In these notes, we will describe recent work on globally solving quasilinear wave equations in the presence of trapped rays, on Kerr-de Sitter space, and obtaining the asymptotic behavior of solutions. For the associated linear problem without trapping, one would consider a global, non-elliptic, Fredholm framework; in the presence of trapping the same framework is available for spaces of growing functions only. In order to solve the quasilinear problem we thus combine these frameworks with the normally hyperbolic trapping results of Dyatlov and a Nash-Moser iteration scheme.
LA - eng
KW - semiclassical resolvent estimates; trapping; normal hyperbolicity; propagation of singularities; b-calculus
UR - http://eudml.org/doc/275534
ER -

References

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