On the radius of spatial analyticity for solutions of the Dirac-Klein-Gordon equations in two space dimensions

Abstract

We consider the initial value problem for the Dirac-Klein-Gordon equations in two space dimensions. Global regularity for $C^{\infty }$ data was proved by Grünrock and Pecher. Here we consider analytic data, proving that if the initial radius of analyticity is ${\sigma }_0>0$, then for later times $t>0$ the radius of analyticity obeys a lower bound $\sigma (t)\ge {\sigma }_0\exp (-At)$. This provides information about the possible dynamics of the complex singularities of the holomorphic extension of the solution at time $t$. The proof relies on an analytic version of Bourgain's Fourier restriction norm method, multilinear space-time estimates of null form type and an approximate conservation of charge.

21 pages. To appear in Annales de l'Institut Henri Poincare / Analyse non lineaire

References in corpus (1)

• Transference of Bilinear Restriction Estimates to Quadratic Variation Norms and the Dirac-Klein-Gordon System