Optimal decay rate of the bipolar Euler-Poisson system with damping in ℝ³

2013/07/08 by Wu, Zhigang, Qun, Yuming
#35B40 #35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1307.2081

Abstract

By rewriting a bipolar Euler-Poisson equations with damping into an Euler equation with damping coupled with an Euler-Poisson equation with damping, and using a new spectral analysis, we obtain the optimal decay results of the solutions in L²-norm, which improve theose in \citeLi3, Wu3. More precisely, the velocities u₁,u₂ decay at the L²-rate (1+t)^-54, which is faster than the normal L²-rate (1+t)^-34 for the Heat equation and the Navier-Stokes equations. In addition, the disparity of two densities ρ₁-ρ₂ and the disparity of two velocities u₁-u₂ decay at the L²-rate (1+t)^-2.

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