Asymptotic limits of the Euler–Poisson equations for dissipative measure-valued solutions

Abstract

We prove that the dissipative measure-valued solutions of the 3D compressible Euler–Poisson equations converge to the solution of the incompressible Euler equations in an asymptotic regime, where the Mach number and Debye length tend to zero simultaneously. Furthermore, the convergence rates are also obtained.

Keywords:

• Euler–Poisson system
• quasineutral limit
• low Mach number limit
• incompressible Euler equations
• measure-valued solution

Mathematics Subject Classifications:

• 35B25
• 35Q35

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China [grant number 12061040] and Key project of Henan Provincial Natural Science Foundation [grant number 232300421143].