Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	James Colliander Justin Holmer Nikolaos Tzirakis

Affiliation:	Department of Mathematics, University of Toronto, 40 St. George St., Toronto, Ontario, Canada M5S 2E4 Justin Holmer ; Department of Mathematics, University of California, Berkeley, Berkeley, California 94720 Nikolaos Tzirakis ; Department of Mathematics, University of Toronto, 40 St. George St., Toronto, Ontario, Canada M5S 2E4

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 $u:mathbb{R}_x^dtimes mathbb{R}_t to mathbb{C}$ and $n:mathbb{R}^d_xtimes mathbb{R}_tto mathbb{R}$ . The Zakharov system is known to be locally well-posed in $(u,n)in L^2times H^{-1/2}$ and the Klein-Gordon-Schrödinger system is known to be locally well-posed in . 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 norm of and controlling the growth of via the estimates in the local theory.

Keywords:	Zakharov system, Klein-Gordon-Schr" odinger system, global well-posedness

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