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

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dc.creatorColliander, Jim
dc.creatorHolmer, Justin
dc.creatorTzirakis, Nikolaos
dc.date2006-03-27
dc.date.accessioned2026-07-07T07:07:13Z
dc.date.available2026-07-07T07:07:13Z
dc.descriptionWe prove low-regularity global well-posedness for the 1d Zakharov system and 3d Klein-Gordon-Schrödinger system, which are systems in two variables $u:\mathbb{R}_x^d\times \mathbb{R}_t \to \mathbb{C}$ and $n:\mathbb{R}^d_x\times \mathbb{R}_t\to \mathbb{R}$. The Zakharov system is known to be locally well-posed in $(u,n)\in L^2\times H^{-1/2}$ and the Klein-Gordon-Schrödinger system is known to be locally well-posed in $(u,n)\in L^2\times L^2$. 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 $L^2$ norm of $u$ and controlling the growth of $n$ via the estimates in the local theory.
dc.identifierhttps://arxiv.org/abs/math/0603595
dc.identifierhttp://arxiv.org/abs/math/0603595
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110312
dc.subjectAnalysis of PDEs
dc.titleLow regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems
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