The Cauchy Problem for the Euler–Poisson System and Derivation of the Zakharov–Kuznetsov Equation
By David Lannes, Felipe Linares, Jean-Claude Saut. 2012
149 citations recorded by the source corpus.
We consider in this paper the rigorous justification of the Zakharov–Kuznetsov equation from the Euler–Poisson system for uniformly magnetized plasmas. We first provide a proof of the local well-posedness of the Cauchy problem for the aforementioned system in dimensions two and three. Then we prove that the long-wave small-amplitude limit is described by the Zakharov–Kuznetsov equation. This is done first in the case of cold plasma; we then show how to extend this result in presence of the isothermal pressure term with uniform estimates when this latter goes to zero.
Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/be9d96ee49eeeb5010069460855dbf478c49f74f
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Computational Mechanics
In Mathematical Physics
Citations in the corpus
- The Fourier restriction norm method for the Zakharov-Kuznetsov equation (2013, methodology): “A rigorous justification of equation (1) from the Euler-Poisson system for a uniformly magnetized plasma, valid in both considered space dimensions, was given very recently by Lannes, Linares, and Saut in [14].”