279 citations · 1.4k across the 39 of their papers we have counts for
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math.AP2020★ 7 cited
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…
math.AP2020★ 8 cited
Global wellposedness for the energy-critical Zakharov system below the ground state
Timothy Candy, Sebastian Herr, Kenji Nakanishi
The Cauchy problem for the Zakharov system in the energy-critical dimension is considered. We prove that global well-posedness holds in the full (non-radial) energy space for…
math.AP2020★ 17 cited
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…