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Pointwise estimates of solutions for the multi-dimensional bipolar Euler–Poisson system

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Abstract

In the paper, we consider a multi-dimensional bipolar hydrodynamic model from semiconductor devices and plasmas. This system takes the form of Euler–Poisson with electric field and frictional damping added to the momentum equations. By making a new analysis on Green’s functions for the Euler system with damping and the Euler–Poisson system with damping, we obtain the pointwise estimates of the solution for the multi-dimensions bipolar Euler–Poisson system. As a by-product, we extend decay rates of the densities \({\rho_i(i=1,2)}\) in the usual L 2-norm to the L p-norm with \({p\geq1}\) and the time-decay rates of the momentums m i (i = 1,2) in the L 2-norm to the L p-norm with p > 1 and all of the decay rates here are optimal.

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Authors and Affiliations

  1. Department of Applied Mathematics, Donghua University, Shanghai, 201620, People’s Republic of China

    Zhigang Wu

  2. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, People’s Republic of China

    Yeping Li

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  1. Zhigang Wu
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  2. Yeping Li
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Correspondence to Yeping Li.

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Wu, Z., Li, Y. Pointwise estimates of solutions for the multi-dimensional bipolar Euler–Poisson system. Z. Angew. Math. Phys. 67, 50 (2016). https://doi.org/10.1007/s00033-016-0651-1

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  • DOI: https://doi.org/10.1007/s00033-016-0651-1

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