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.
@incollection{JEDP_2014____A10_0, author = {Peter Hintz and Andr\'as Vasy}, title = {Quasilinear waves and trapping: {Kerr-de} {Sitter} space}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {10}, pages = {1--15}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2014}, doi = {10.5802/jedp.113}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.113/} }
TY - JOUR AU - Peter Hintz AU - András Vasy TI - Quasilinear waves and trapping: Kerr-de Sitter space JO - Journées équations aux dérivées partielles PY - 2014 SP - 1 EP - 15 PB - Groupement de recherche 2434 du CNRS UR - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.113/ DO - 10.5802/jedp.113 LA - en ID - JEDP_2014____A10_0 ER -
%0 Journal Article %A Peter Hintz %A András Vasy %T Quasilinear waves and trapping: Kerr-de Sitter space %J Journées équations aux dérivées partielles %D 2014 %P 1-15 %I Groupement de recherche 2434 du CNRS %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.113/ %R 10.5802/jedp.113 %G en %F JEDP_2014____A10_0
Peter Hintz; András Vasy. Quasilinear waves and trapping: Kerr-de Sitter space. Journées équations aux dérivées partielles (2014), article no. 10, 15 p. doi : 10.5802/jedp.113. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.113/
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