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math.AP2021★ 1 cited
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…
math.AP2021
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…
math.AP2021
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…