{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/60203"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/60203","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Radiation field for Einstein vacuum equations","abstract":"The radiation field introduced by Friedlander provides a direct approach to the asymptotic expansion of solutions to the wave equation near null infinity. We use this concept to study the asymptotic behavior of solutions to the Einstein Vacuum equations, which are close to Minkowski space, at null infinity. By imposing harmonic gauge, the Einstein Vacuum equations reduce to a system of quasilinear wave equations on R\"j\". We show that if the space dimension n > 5 the Moller wave operator is an isomorphism from Cauchy data satisfying the constraint equations to the radiation fields satisfying the corresponding constraint equations on small neighborhoods of suitable weighted b-type Sobolev spaces.","abstract_html":"The radiation field introduced by Friedlander provides a direct approach to the asymptotic expansion of solutions to the wave equation near null infinity. We use this concept to study the asymptotic behavior of solutions to the Einstein Vacuum equations, which are close to Minkowski space, at null infinity. By imposing harmonic gauge, the Einstein Vacuum equations reduce to a system of quasilinear wave equations on R"j". We show that if the space dimension n > 5 the Moller wave operator is an isomorphism from Cauchy data satisfying the constraint equations to the radiation fields satisfying the corresponding constraint equations on small neighborhoods of suitable weighted b-type Sobolev spaces.","abstract_has_math":false,"creators":["Wang, Fang, Ph. D. Massachusetts Institute of Technology"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Dept. of Mathematics.","school":null,"contributors":[],"advisors":["Richard B. Melrose."],"committee_chairs":[],"committee_members":[],"year":2010,"date_issued":"2010","date_published":"2010","updated_at":"2026-07-22T22:21:19Z","subjects":["Mathematics."],"languages":["eng"],"rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/60203","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Richard B. Melrose."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Dept. of Mathematics."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. Dept. of Mathematics."]},{"key":"dc:creator","label":"Author","values":["Wang, Fang, Ph. D. 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They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://dspace.mit.edu/handle/1721.1/7582"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1721.1/60203"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 77-78)."]},{"key":"dc:description.abstract","label":"Abstract","values":["The radiation field introduced by Friedlander provides a direct approach to the asymptotic expansion of solutions to the wave equation near null infinity. We use this concept to study the asymptotic behavior of solutions to the Einstein Vacuum equations, which are close to Minkowski space, at null infinity. By imposing harmonic gauge, the Einstein Vacuum equations reduce to a system of quasilinear wave equations on R\"j\". We show that if the space dimension n > 5 the Moller wave operator is an isomorphism from Cauchy data satisfying the constraint equations to the radiation fields satisfying the corresponding constraint equations on small neighborhoods of suitable weighted b-type Sobolev spaces."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["Radiation field for Einstein vacuum equations"]}]}],"canonical_facts":{"dc:contributor.advisor":["Richard B. Melrose."],"dc:contributor.department":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:contributor.other":["Massachusetts Institute of Technology. Dept. of Mathematics."],"dc:creator":["Wang, Fang, Ph. D. Massachusetts Institute of Technology"],"dc:date.accessioned":["2010-12-06T17:37:34Z"],"dc:date.available":["2010-12-06T17:37:34Z"],"dc:date.issued":["2010"],"dc:description":["Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.","Cataloged from PDF version of thesis.","Includes bibliographical references (p. 77-78)."],"dc:description.abstract":["The radiation field introduced by Friedlander provides a direct approach to the asymptotic expansion of solutions to the wave equation near null infinity. We use this concept to study the asymptotic behavior of solutions to the Einstein Vacuum equations, which are close to Minkowski space, at null infinity. By imposing harmonic gauge, the Einstein Vacuum equations reduce to a system of quasilinear wave equations on R\"j\". We show that if the space dimension n > 5 the Moller wave operator is an isomorphism from Cauchy data satisfying the constraint equations to the radiation fields satisfying the corresponding constraint equations on small neighborhoods of suitable weighted b-type Sobolev spaces."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/60203"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission."],"dc:rights.uri":["http://dspace.mit.edu/handle/1721.1/7582"],"dc:subject":["Mathematics."],"dc:title":["Radiation field for Einstein vacuum equations"],"dc:type":["Thesis"]},"updated_at":"2026-07-22T22:21:19Z"}