Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems

James Colliander, Justin Holmer, Nikolaos Tzirakis

Research output: Contribution to journalArticlepeer-review

Abstract

We prove low regularity global well-posedness for the 1d Zakharov system and the 3d Klein-Gordon-Schrödinger system, which are systems in two variables u : ℝd x x ℝt → C and n : ℝd x × ℝt → ℝ. The Zakharov system is known to be locally well-posed in (u, n) ε L 2, ×H-1/2 and the Klein-Gordon- Schrödinger system is known to be locally well-posed in (u, n) ε L2× L2. Here, we show that the Zakharov and Klein-Gordon-Schrödinger systems are globally well-posed in these spaces, respectively, by using an available conservation law for the L2 norm of u and controlling the growth of n via the estimates in the local theory.

Original languageEnglish (US)
Pages (from-to)4619-4638
Number of pages20
JournalTransactions of the American Mathematical Society
Volume360
Issue number9
DOIs
StatePublished - Sep 2008

Keywords

  • Global wellposedness
  • Klein-gordon-schödinger system
  • Zakharov system

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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