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Global smooth solutions to the multi-dimensional hydrodynamic model for two-carrier plasmas. (English) Zbl 1020.35072
Summary: The existence of global smooth solutions to the multidimensional hydrodynamic model for plasmas of electrons and positively charged ions is shown under the assumption that the initial densities are close to a constant. The model consists of the conservation laws for the particle densities and the current densities, coupled to the Poisson equation for the electrostatic potential. Furthermore, it is proved that the particle densities converge exponentially fast to the (constant) steady state. The proof uses a higher-order energy method inspired from extended thermodynamics.

##### MSC:
 35Q35 PDEs in connection with fluid mechanics 82D10 Statistical mechanical studies of plasmas 76X05 Ionized gas flow in electromagnetic fields; plasmic flow
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