On the global well-posedness of energy-critical Schrodinger equations in curved spaces
Original manuscript September 8, 2010
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Mathematical Sciences Publishers
2013
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| Online Access: | http://hdl.handle.net/1721.1/80820 https://orcid.org/0000-0002-8220-4466 |
| _version_ | 1811078313788047360 |
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| author | Ionescu, Alexandru Pausader, Benoit Staffilani, Gigliola |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Ionescu, Alexandru Pausader, Benoit Staffilani, Gigliola |
| author_sort | Ionescu, Alexandru |
| collection | MIT |
| description | Original manuscript September 8, 2010 |
| first_indexed | 2024-09-23T10:57:38Z |
| format | Article |
| id | mit-1721.1/80820 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:57:38Z |
| publishDate | 2013 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | mit-1721.1/808202022-10-01T00:13:08Z On the global well-posedness of energy-critical Schrodinger equations in curved spaces Ionescu, Alexandru Pausader, Benoit Staffilani, Gigliola Massachusetts Institute of Technology. Department of Mathematics Staffilani, Gigliola Original manuscript September 8, 2010 In this paper we present a method to study global regularity properties of solutions of large-data critical Schrodinger equations on certain noncompact Riemannian manifolds. We rely on concentration compactness arguments and a global Morawetz inequality adapted to the geometry of the manifold (in other words we adapt the method of Kenig and Merle to the variable coefficient case), and a good understanding of the corresponding Euclidean problem (a theorem of Colliander, Keel, Staffilani, Takaoka and Tao). As an application we prove global well-posedness and scattering in H[superscript 1] for the energy-critical defocusing initial-value problem (i∂t + Δ[subscript g])u = u|u|[superscript 4], u(0) = ϕ, on hyperbolic space ℍ[superscript 3]. National Science Foundation (U.S.) (Grant DMS 0602678) 2013-09-20T13:38:09Z 2013-09-20T13:38:09Z 2012-11 2010-08 Article http://purl.org/eprint/type/JournalArticle 1948-206X 2157-5045 http://hdl.handle.net/1721.1/80820 Ionescu, Alexandru, Benoit Pausader, and Gigliola Staffilani. “On the global well-posedness of energy-critical Schrödinger equations in curved spaces.” Analysis & PDE 5, no. 4 (November 27, 2012): 705-746. https://orcid.org/0000-0002-8220-4466 en_US http://dx.doi.org/10.2140/apde.2012.5.705 Analysis & PDE Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Mathematical Sciences Publishers arXiv |
| spellingShingle | Ionescu, Alexandru Pausader, Benoit Staffilani, Gigliola On the global well-posedness of energy-critical Schrodinger equations in curved spaces |
| title | On the global well-posedness of energy-critical Schrodinger equations in curved spaces |
| title_full | On the global well-posedness of energy-critical Schrodinger equations in curved spaces |
| title_fullStr | On the global well-posedness of energy-critical Schrodinger equations in curved spaces |
| title_full_unstemmed | On the global well-posedness of energy-critical Schrodinger equations in curved spaces |
| title_short | On the global well-posedness of energy-critical Schrodinger equations in curved spaces |
| title_sort | on the global well posedness of energy critical schrodinger equations in curved spaces |
| url | http://hdl.handle.net/1721.1/80820 https://orcid.org/0000-0002-8220-4466 |
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