Pointwise Estimates for Bipolar Compressible Navier–Stokes–Poisson System in Dimension Three
Pointwise Estimates for Bipolar Compressible Navier–Stokes–Poisson System in Dimension Three
复制标题
DOI：
10.1007/s00205-017-1140-1
复制
发表时间：
2017-06
影响因子：
2.5
通讯作者：
Zhigang Wu;Weike Wang
中科院分区：
文献类型：
--
作者：
Zhigang Wu;Weike Wang
考虑三维双极Navier-Stokes-Poisson方程组（1.1）的Cauchy问题.我们得到了解的时间渐近形状的逐点估计，它表现出与Navier-Stokes系统一样的广义Huygens原理。这种现象是与单极Navier-Stokes-Poisson系统最重要的区别。由于系统（1.1）的非保守结构和抵消电场（非局部项）影响的两个载流子的相互作用，一些新的观察对于证明是必不可少的。我们充分利用了系统总密度和总动量的守恒结构，利用了线性化单极Navier-Stokes-Poisson系统的机制以及系统中密度差和动量差的非线性项的特殊形式.最后，作为副产品，我们将通常的衰减率扩展到衰减率，并提高了以前的衰减率。
The Cauchy problem of the bipolar Navier–Stokes–Poisson system (1.1) in dimension three is considered. We obtain the pointwise estimates of the time-asymptotic shape of the solution, which exhibit a generalized Huygens’ principle as the Navier–Stokes system. This phenomenon is the most important difference from the unipolar Navier–Stokes–Poisson system. Due to the non-conservative structure of the system (1.1) and the interplay of two carriers which counteract the influence of the electric field (a nonlocal term), some new observations are essential for the proof. We fully use the conservative structure of the system for the total density and total momentum, and the mechanism of the linearized unipolar Navier–Stokes–Poisson system together with the special form of the nonlinear terms in the system for the difference of densities and the difference of momentums. Lastly, as a byproduct, we extend the usual-decay rate to the-decay rate withand also improve former decay rates.