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Global convergence of an isentropic Euler-Poisson \\[2mm] system in $\R^+ \times \R^d$
Keywords:Euler-Poisson system, uniform global smooth solution, energy estimate, compactness and convergence.
Abstract:
      We prove the global-in-time convergence of an Euler-Poisson system near a constant equilibrium state in the whole space $\R^d$, as physical parameters tend to zero. The result follows from the uniform global existence of smooth solutions by means of energy estimates together with compactness arguments. For this purpose, we establish uniform estimates for $\dive \,u$ and $\curle \,u$ instead of $\nabla u$.