Global existence and L^p convergence rates of planar waves for three-dimensional bipolar Euler-Poisson systems

2015/01/24 by Jie Liao, Liao, Jie, Yeping Li +1
Mathematics · #35M20 #35Q35 #76W05 #Advanced Mathematical Physics Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1501.06008

openalex publication_date 2015/01/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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. We show the global existence and L^p convergence rates of planar diffusion waves for multi-dimensional bipolar Euler-Poisson systems when the initial data are near the planar diffusive waves. A frequency decomposition and approximate Green function based on delicate energy method are used to get the optimal decay rates of the planar diffusion waves. To our knowledge, the L^p(p∈[2,+∞])-convergence rate of planar waves improves the previous results about the L²-convergence rates.

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