Dynamics of Partial Differential Equations

Volume 11 (2014)

Number 3

Global well-posedness for the critical Schrödinger-Debye system

Pages: 251 – 268

DOI: https://dx.doi.org/10.4310/DPDE.2014.v11.n3.a3

Authors

Xavier Carvajal (Instituto de Matemática, Universidade Federal do Rio de Janeiro, Brazil)

Pedro Gamboa (Instituto de Matemática, Universidade Federal do Rio de Janeiro, Brazil)

Abstract

We establish global well-posedness results for the initial value problem associated to the Schrödinger-Debye system in dimension two, for data in $H^s(\mathbb{R}^2) \times L^2(\mathbb{R}^2), 2 / 3 \lt s \leq 1$ and for data in $H^1(\mathbb{R}^2) \times H^1(\mathbb{R}^2)$.

Keywords

Schrödinger-Debye system, global well-posedness, a priori estimates

2010 Mathematics Subject Classification

35A01, 35Q53

Published 19 September 2014