From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov

Daniel Han-Kwan (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

We introduce a long wave scaling for the Vlasov-Poisson equation and derive, in the cold ions limit, the Korteweg-De Vries equation (in 1D) and the Zakharov-Kuznetsov equation (in higher dimensions, in the presence of an external magnetic field). The proofs are based on the relative entropy method.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Daniel Han-Kwan. From Vlasov-Poisson to Korteweg-de Vries and Zakharov-Kuznetsov. 2012. ⟨hal-00732390⟩