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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
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