Advances in Differential Equations

Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in five and higher dimensions

Isao Kato and Shinya Kinoshita

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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 $d \ge 5$.

Article information

Source
Adv. Differential Equations, Volume 23, Number 9/10 (2018), 725-750.

Dates
First available in Project Euclid: 13 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.ade/1528855477

Mathematical Reviews number (MathSciNet)
MR3813998

Zentralblatt MATH identifier
06973943

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35B40: Asymptotic behavior of solutions 35A01: Existence problems: global existence, local existence, non-existence 35A02: Uniqueness problems: global uniqueness, local uniqueness, non- uniqueness

Citation

Kato, Isao; Kinoshita, Shinya. Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in five and higher dimensions. Adv. Differential Equations 23 (2018), no. 9/10, 725--750. https://projecteuclid.org/euclid.ade/1528855477


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