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Smooth irrotational flows in the large to the Euler-Poisson system in $$\mathbb{R}^{3+1}$$. (English) Zbl 0929.35112
The paper deals with a simple two-fluid model describing the dynamics of a plasma by means of the Euler-Poisson system, where the compressible electron field interacts with its own electric field against a constant charged ion background. The existence of a unique global solution of the Euler-Poisson system is proved. Global smooth irrotational flows are constructed with small velocity of the electron fluid.

MSC:
 35Q35 PDEs in connection with fluid mechanics 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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