Large time behavior of solutions to 3D compressible Navier-Stokes-Poisson system |
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Authors: | HaiLiang Li Ting Zhang |
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Affiliation: | 1. Department of Mathematics and Institute of Mathematics and Interdisciplinary Science, Capital Normal University, Beijing, 100048, China 2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China
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Abstract: | We consider the three-dimensional compressible Navier-Stokes-Poisson system where the electric field of the internal electrostatic potential force is governed by the self-consistent Poisson equation. If the Fourier modes of the initial data are degenerate at the low frequency or the initial data decay fast at spatial infinity, we show that the density converges to its equilibrium state at the L 2-rate $(1 + t)^{ - tfrac{7} {4}}$ or L ??-rate $(1 + t)^{ - tfrac{5} {2}}$ , and the momentum decays at the L 2-rate $(1 + t)^{ - tfrac{5} {4}}$ or L ??-rate (1 + t)?2. These convergence rates are shown to be optimal for the compressible Navier-Stokes-Poisson system. |
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Keywords: | compressible Navier-Stokes-Poisson system optimal decay rate |
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