17 citations · 83 across the 17 of their papers we have counts for
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Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations in almost critical spaces
Hiroyuki Hirayama, Shinya Kinoshita, Mamoru Okamoto
In this paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrödinger equations introduced by Colin and Colin (2004). We determine an almost opt…
The Zakharov-Kuznetsov equation in high dimensions: Small initial data of critical regularity
Sebastian Herr, Shinya Kinoshita
The Zakharov-Kuznetsov equation in spatial dimension is considered. The Cauchy problem is shown to be globally well-posed for small initial data in critical spaces and it…
Loomis-Whitney-type inequalities and low regularity well-posedness of the periodic Zakharov-Kuznetsov equation
Shinya Kinoshita, Robert Schippa
Local well-posedness for the two-dimensional Zakharov-Kuznetsov equation in the fully periodic case with initial data in Sobolev spaces , , is proved. Frequency dependent…
Subcritical well-posedness results for the Zakharov-Kuznetsov equation in dimension three and higher
Sebastian Herr, Shinya Kinoshita
The Zakharov-Kuznetsov equation in space dimension is considered. It is proved that the Cauchy problem is locally well-posed in in the full subcritica…