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Global Well-Posedness of High Dimensional Maxwell-Dirac for Small Critical Data

Cristian Gavrus
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      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.
      Format: Paperback / softback CONTRIBUTORS: Cristian Gavrus EAN: 9781470441111 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2020-10-01 CITY: GENRE: MATHEMATICS / Differential Equations / General WIDTH: 178 cm SPINE:

      Book Themes:

      Differential calculus and equations

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      Cristian Gavrus, University of California, Berkeley, CA.Sung-Jin Oh, Korea Institute for Advanced Study, Seoul, Republic of Korea.
      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.
      Format: Paperback / softback CONTRIBUTORS: Cristian Gavrus EAN: 9781470441111 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2020-10-01 CITY: GENRE: MATHEMATICS / Differential Equations / General WIDTH: 178 cm SPINE:

      Book Themes:

      Differential calculus and equations

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      Be the first to write a review
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      Cristian Gavrus, University of California, Berkeley, CA.Sung-Jin Oh, Korea Institute for Advanced Study, Seoul, Republic of Korea.

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