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Global well-posedness of high dimensional maxwell-dirac for small critical data / Cristian Gavrus, Sung-Jin Oh

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 264, number 1279 (March 2020)Publisher: Providence : American Mathematical Society, March 2020Description: v, 94 Seiten : Diagramme, IllustrationenISBN:
  • 9781470441111
Additional physical formats: 9781470458089 | Erscheint auch als: Global well-posedness of high dimensional maxwell-dirac for small critical data. Online-Ausgabe Providence : American Mathematical Society, 2020. 1 Online-Ressource (v, 94 Seiten)MSC: MSC: 35L45 | 35Q41 | 35Q61RVK: RVK: SI 130DOI: DOI: 10.1090/memo/1279Summary: In this paper, the authors prove global well-posedness of the massless Maxwell-Dirac equation in the Coulomb gauge on \mathbb{R}^{1+d} (d\geq 4) for data with small scale-critical Sobolev norm, as well as modified scattering of the solutions. Main components of the authors' proof are A) uncovering null structure of Maxwell-Dirac in the Coulomb gauge, and B) proving solvability of the underlying covariant Dirac equation. A key step for achieving both is to exploit (and justify) a deep analogy between Maxwell-Dirac and Maxwell-Klein-Gordon (for which an analogous result was proved earlier by Krieger-Sterbenz-Tataru, which says that the most difficult part of Maxwell-Dirac takes essentially the same form as Maxwell-Klein-Gordon.Summary: Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- Chapter 3. Function spaces -- Chapter 4. Decomposition of the nonlinearity -- Chapter 5. Statement of the main estimates -- Chapter 6. Proof of the main theorem -- Chapter 7. Interlude: Bilinear null form estimates -- Chapter 8. Proof of the bilinear estimates -- Chapter 9. Proof of the trilinear estimates -- Chapter 10. Solvability of paradifferential covariant half-wave equations -- Bibliography -- Back Cover.PPN: PPN: 1703308085
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