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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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