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Global classical solutions to the compressible Euler-Maxwell equations. (English) Zbl 1252.35183
The author considers the Cauchy problem in $$\mathbb{R}^{n}$$ ($$n\geq 2$$) for compressible Euler-Maxwell equations. This paper has two purposes. First, the author shows that there exists a unique global classical solution for small initial data in critical Chemin-Lerner spaces. In the second part, the author investigates the limit to zero of some physical parameters in scaled Euler-Maxwell equations.
The main tools used in this study are the Littlewood-Paley decomposition and the weak convergence method.

##### MSC:
 35L45 Initial value problems for first-order hyperbolic systems 35Q31 Euler equations 35Q61 Maxwell equations
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