Optimal Decay Rate of the Compressible Navier–Stokes–Poisson System in $${\mathbb {R}^3}$$
Optimal Decay Rate of the Compressible Navier–Stokes–Poisson System in $${\mathbb {R}^3}$$
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DOI：
10.1007/s00205-009-0255-4
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发表时间：
2008-11
影响因子：
2.5
通讯作者：
Hai-liang Li;A. Matsumura;Guojing Zhang
中科院分区：
文献类型：
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作者：
Hai-liang Li;A. Matsumura;Guojing Zhang
本文考虑可压缩Navier-Stokes-Poisson（NSP）方程，分析了由自洽Poisson方程控制的内部静电势力的电场对解的定性行为的影响.观察到电场的旋转效应影响了流体的分散，降低了溶液的时间衰减速率。事实上，我们证明了NSP系统的密度分别以与可压缩Navier-Stokes系统相同的L2-轨道L ∞-速率（1 +t）−3/2收敛到其平衡态，但NSP系统的动量分别以L2-轨道L ∞-速率（1 +t）− 1衰减，这比可压缩Navier-Stokes系统的L2-轨道L ∞-速率（1 +t）−3/2慢[Duan et al.，在Math Models Methods Appl Sci 17：737-758，2007中; Liu和Wang，在Comm Math Phys 196：145-173，1998中; Matsumura和Nishida，在J Math京都Univ 20：67-104，1980中]和无旋Euler-Poisson系统的L ∞-速率（1 +t）-pwith [Guo，在Comm Math Phys 195：249-265，1998中]。这些收敛速度被证明是最佳的可压缩NSP系统。
The compressible Navier–Stokes–Poisson (NSP) system is considered inin the present paper, and the influences of the electric field of the internal electrostatic potential force governed by the self-consistent Poisson equation on the qualitative behaviors of solutions is analyzed. It is observed that the rotating effect of electric field affects the dispersion of fluids and reduces the time decay rate of solutions. Indeed, we show that the density of the NSP system converges to its equilibrium state at the sameL2-rateorL∞-rate (1 +t)−3/2respectively as the compressible Navier–Stokes system, but the momentum of the NSP system decays at theL2-rateorL∞-rate (1 +t)−1respectively, which is slower than theL2-rateorL∞-rate (1 +t)−3/2for compressible Navier–Stokes system [Duan et al., in Math Models Methods Appl Sci 17:737–758, 2007; Liu and Wang, in Comm Math Phys 196:145–173, 1998; Matsumura and Nishida, in J Math Kyoto Univ 20:67–104, 1980] and theL∞-rate (1 +t)−pwithfor irrotational Euler–Poisson system [Guo, in Comm Math Phys 195:249–265, 1998]. These convergence rates are shown to be optimal for the compressible NSP system.