## Convergence of compressible Euler-Maxwell equations to incompressible Euler equations.(English)Zbl 1145.35054

Summary: We study the combined quasineutral and non-relativistic limit of compressible Euler-Maxwell equations. For well prepared initial data the convergences of solutions of compressible Euler-Maxwell equations to the solutions of incompressible Euler equations are justified rigorously by an analysis of asymptotic expansions and a careful use of $$\varepsilon$$-weighted Lyapunov-type functional. One main ingredient of establishing uniformly a priori estimates with respect to $$\varepsilon$$ is to use the curl-div decomposition of the gradient.

### MSC:

 35C20 Asymptotic expansions of solutions to PDEs 35B40 Asymptotic behavior of solutions to PDEs 35L60 First-order nonlinear hyperbolic equations 35Q35 PDEs in connection with fluid mechanics
Full Text:

### References:

 [1] Besse C., M3AS 14 pp 393– (2004) [2] DOI: 10.1080/03605300008821529 · Zbl 0970.35110 [3] Brenier Y., Comm. Math. Sci. 1 pp 437– (2003) · Zbl 1089.35048 [4] Brézis H., C. R. Acad. Sci. Paris 321 pp 953– (1995) [5] Chen F., Introduction to Plasma Physics and Controlled Fusion 1 (1984) [6] DOI: 10.1080/00411450008205877 · Zbl 1019.82023 [7] DOI: 10.1080/03605300008821542 · Zbl 0978.82086 [8] DOI: 10.1016/0022-1236(72)90003-1 · Zbl 0229.76018 [9] DOI: 10.1002/cpa.3160340405 · Zbl 0476.76068 [10] DOI: 10.1002/cpa.3160350503 · Zbl 0478.76091 [11] Majda A., Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables (1984) · Zbl 0537.76001 [12] DOI: 10.1007/BF00251436 · Zbl 0187.49508 [13] Peng Y. J., Asymptotic Anal. 41 pp 141– (2005) [14] DOI: 10.1007/s11401-005-0556-3 · Zbl 1145.35347 [15] Rishbeth H., Introduction to Ionospheric Physics (1969) [16] DOI: 10.1006/jdeq.1994.1157 · Zbl 0838.35071 [17] DOI: 10.1007/s00332-001-0004-9 [18] DOI: 10.1081/PDE-120030403 · Zbl 1140.35551 [19] DOI: 10.1080/03605300500361487 · Zbl 1137.35416
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.