2 citations · 3 across the 7 of their papers we have counts for
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A remark on the Half wave Schrödinger equation in the energy space
Isao Kato
We investigate the Cauchy problem for the half wave Schrödinger equation in the energy space. We derive the local well-posedness in the energy space for the odd power type nonlinea…
Ill-posedness for the Half wave Schrödinger equation
Isao Kato
We study ill-posedness for the half wave Schrödinger equation introduced by Xu \cite{Xu}. Ill-posedness is obtained in the super-critical or at the critical space. The proof is bas…
Local well-posedness of a system describing laser-plasma interactions
Sebastian Herr, Isao Kato, Shinya Kinoshita +1
A degenerate Zakharov system arises as a model for the description of laser-plasma interactions. It is a coupled system of a Schrödinger and a wave equation with a non-dispersive d…
Local well-posedness of the Cauchy problem for the degenerate Zakharov system
Isao Kato
The aim of this paper is to investigate well-posedness of the Cauchy problem for the degenerate Zakharov system. Local well-posedness holds for anisotropic Sobolev data by applying…
Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in five and more dimensions
Isao Kato, Shinya Kinoshita
We study the Cauchy problem of the Klein-Gordon-Zakharov system in spatial dimension with initial datum $(u, \partial_t u, n, \partial_t n)|_{t=0} \in H^{s+1}(\mathbb{R}^…
Well-posedness for the Cauchy problem of the Klein-Gordon-Zakharov system in four and more spatial dimensions
Isao Kato
We study the Cauchy problem for the Klein-Gordon-Zakharov system in spatial dimension with radial or non-radial initial datum $(u, \partial_t u, n, \partial_t n)|_{t=0}\i…
Scattering and well-posedness for the Zakharov system at a critical space in four and more spatial dimensions
Isao Kato, Kotaro Tsugawa
We study the Cauchy problem for the Zakharov system in spatial dimension with initial datum $(u(0), n(0), \partial_t n(0)) \in H^k(\mathbb{R}^d) \times \dot{H}^l(\mathbb{R…