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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.

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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