The zero-electron-mass limit in the Euler-Poisson system with non-constant ion density for all time
Abstract
This paper is devoted to investigating the zero-electron-mass limit of a one-fluid Euler-Poisson system with non-constant ion density. We give a rigorous proof of the global convergence in time to the incompressible type Euler equations for smooth solution if the initial perturbation is uniformly small. The idea is based on uniform energy estimates and compactness arguments on the solutions. In particular, we first employ a key technique of antisymmetric matrix to handle the singular terms in the system and obtain uniform estimates of the time derivatives. Then, we develop an induction argument on the order of space derivatives to complete the energy estimates.
Fields of Study & Subjects
Navier-Stokes equation solutions
Stability and Controllability of Differential Equations
Thermoelastic and Magnetoelastic Phenomena
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems - B
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 41
- Issue
- 0
- Pages
- 1–23
- Publication date
- 1 January 2026