TY - JOUR
T1 - Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems
AU - Colliander, James
AU - Holmer, Justin
AU - Tzirakis, Nikolaos
N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.
PY - 2008/9
Y1 - 2008/9
N2 - 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.
AB - 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.
KW - Global wellposedness
KW - Klein-gordon-schödinger system
KW - Zakharov system
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U2 - 10.1090/S0002-9947-08-04295-5
DO - 10.1090/S0002-9947-08-04295-5
M3 - Article
AN - SCOPUS:67650754033
SN - 0002-9947
VL - 360
SP - 4619
EP - 4638
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 9
ER -