ZK‐type limit for the Euler–Poisson system with a realistic electrostatic potential in dimension three

Abstract

We explore the Zakharov–Kuznetsov‐type limit for the three‐dimensional Euler–Poisson systems with external magnetic fields when the plasma has a realistic electrostatic potential. It reveals that both homogeneous and inhomogeneous Zakharov–Kuznetsov‐type equations can be obtained from the Euler–Poisson system through the application of the Gardner–Morikawa transformation. By analyzing the remaining system, we employ the energy method within Sobolev spaces to provide estimates, leading to the emergence of Zakharov–Kuznetsov‐type dynamics over a time interval of the order .