The Fourier restriction norm method for the Zakharov-Kuznetsov equation

By Axel Grunrock, Sebastian Herr. 2013

102 citations recorded by the source corpus.

The Cauchy problem for the Zakharov-Kuznetsov equation is shown to be locally well-posed in $H^s(\mathbb{R}^2)$ for all $s>\frac{1}{2}$ by using the Fourier restriction norm method and bilinear refinements of Strichartz type inequalities.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/70b9612903b94bb00a121bcd434e68dcaf030333

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In Applied Mathematics

1. Didier Pilod
2. S. Kinoshita
3. Luc Molinet
4. Carlos E. Kenig
5. Yue Liu
6. Baoxiang Wang
7. Yvan Martel
8. Ademir Fernando Pazoto

In Mathematical Physics

1. Didier Pilod
2. S. Kinoshita
3. Luc Molinet
4. Carlos E. Kenig
5. Yue Liu
6. Baoxiang Wang
7. Yvan Martel
8. Zhaoyang Yin

Citations in the corpus

• Bilinear Strichartz estimates for the Zakharov–Kuznetsov equation and applications (2013, result): “We saw very recently on the arXiv that Grünrock and Herr obtained a similar result [5] in the R(2) case by using the same kind of techniques.”
• Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation in 2D (2019, methodology): “In the 2D case, Grünrock and Herr in [6], and Molinet and”