Global smooth solutions to the multi-dimensional hydrodynamic model for two-carrier plasmas |
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Institution: | a Instituto per le Applicazioni del Calcolo Consiglio Nazionale delle Ricerche, 80131 Napoli, Italy b Fachbereich Mathematik und Statistik, Universität Konstanz, 78457 Konstanz, Germany |
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Abstract: | The existence of global smooth solutions to the multi-dimensional 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. |
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Keywords: | Hydrodynamic model Global existence of smooth solutions Exponential stability of steady states Long-time behavior of solutions Plasmas Thermodynamical energy |
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