From quantum Euler–Maxwell equations to incompressible Euler equations

Abstract

The combined quasi-neutral and non-relativistic limit of compressible quantum Euler–Maxwell equations for plasmas is studied in this paper. For well-prepared initial data, it is shown that the smooth solution of compressible quantum Euler–Maxwell equations converges to the smooth solution of incompressible Euler equations by using the modulated energy method. Furthermore, the associated convergence rates are also obtained.

Keywords:

• quantum Euler–Maxwell equations
• incompressible Euler equations
• asymptotic limit
• modulated energy function

AMS Subject Classifications:

• 35B40
• 35C20
• 35Q35
• 76Y05

Notes

J. Yang’s research was partially supported by the Joint Funds of the National Natural Science Foundation of China [grant number U1204103], China Postdoctoral Science Foundation Funded Project [grant number 2013M530032] and the science and technology research projects of Education Department of Henan province [grant number 13A110731].