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September/October 2018 Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in five and higher dimensions
Isao Kato, Shinya Kinoshita
Adv. Differential Equations 23(9/10): 725-750 (September/October 2018).

Abstract

We study the Cauchy problem of the Klein-Gordon-Zakharov system in spatial dimension $d \ge 5$ with initial datum $(u, \partial_t u, n, \partial_t n)|_{t=0} \in H^{s+1}(\mathbb{R}^d) \times H^s(\mathbb{R}^d) \times \dot{H}^s(\mathbb{R}^d) \times \dot{H}^{s-1} (\mathbb{R}^d)$. The critical value of $s$ is $s_c=d/2-2$. By $U^2, V^2$ type spaces, we prove that the small data global well-posedness and scattering hold at $s=s_c$ in $d \ge 5$.

Citation

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Isao Kato. Shinya Kinoshita. "Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in five and higher dimensions." Adv. Differential Equations 23 (9/10) 725 - 750, September/October 2018.

Information

Published: September/October 2018
First available in Project Euclid: 13 June 2018

zbMATH: 06973943
MathSciNet: MR3813998

Subjects:
Primary: 35A01, 35A02, 35B40, 35Q55

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.23 • No. 9/10 • September/October 2018
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