Global well-posedness of high dimensional Maxwell-Dirac for small critical data /

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) uncover...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Gavrus, Cristian (Cristian Dan) (Author), Oh, Sung-Jin (Author)
Format: Electronic eBook
Language:Inglés
Published: Providence, RI : American Mathematical Society, [2020]
Series:Memoirs of the American Mathematical Society ; no. 1279.
Subjects:
Differential equations, Partial.
Maxwell equations.
Dirac equation.
Initial value problems.
Exponential functions.
Équations aux dérivées partielles.
Équations de Maxwell.
Équation de Dirac.
Problèmes aux valeurs initiales.
Fonctions exponentielles.
Ecuaciones diferenciales
Ecuaciones en derivadas parciales
Funciones exponenciales
Differential equations, Partial
Dirac equation
Exponential functions
Initial value problems
Maxwell equations
Partial differential equations > Hyperbolic equations and systems [See also 58J45] > Initial value problems for first-order hyperbolic systems.
Partial differential equations > Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] > Time-dependent Schrödinger equations, Dirac equat.
Partial differential equations > Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] > Maxwell equations.
Online Access:Texto completo
Table of Contents:
  • Preliminaries
  • Function spaces
  • Decomposition of the nonlinearity
  • Statement of the main estimates
  • Proof of the main theorem
  • Interlude : Bilinear null form estimates
  • Proof of the bilinear estimates
  • Proof of the trilinear estimates
  • Solvability of paradifferential covariant half-wave equations.

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