Pointwise space-time estimates of two-phase fluid model in dimension three
Pointwise space-time estimates of two-phase fluid model in dimension three
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DOI：
10.1007/s00028-024-00943-0
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发表时间：
2021-11
影响因子：
1.4
通讯作者：
Zhigang Wu;W. Zhou
中科院分区：
文献类型：
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作者：
Zhigang Wu;W. Zhou
我们研究了Choi（SIAM J Math Anal 48：3090-3122，2016）导出的两相流体模型柯西问题经典解的逐点时空行为，当初始数据足够小且规则时。该模型是可压缩阻尼欧拉系统与可压缩Naiver-Stokes系统通过阻力耦合。如我们所知，Liu和Wang（Commun Math Phys 196：145-173，1998）验证了可压缩Naiver-Stokes系统的解服从广义惠更斯原理，而Wang和Yang（J Differ Equ 173：410-450，2001）验证了可压缩Euler系统的解由于阻尼机制而不服从广义惠更斯原理。本文证明了两相流体模型的两个密度和两个动量都服从Liu和Wang（Commun Math Phys 196：145-173，1998）中的广义惠更斯原理。其主要贡献是克服了系统阻尼机制引起的不守恒的困难。作为副产品，我们还扩展了Wu等人（SIAM J Math Anal 52（6）：5748-5774，2020）中的估计，以估计。
We studied the pointwise space-time behavior of the classical solution to the Cauchy problem of two-phase fluid model derived by Choi (SIAM J Math Anal 48:3090–3122, 2016) when the initial data is sufficiently small and regular. This model is the compressible damped Euler system coupled with the compressible Naiver–Stokes system via a drag force. As we know, Liu and Wang (Commun Math Phys 196:145–173, 1998) verified that the solution of the compressible Naiver–Stokes system obeys the generalized Huygens’ principle, while Wang and Yang (J Differ Equ 173:410–450, 2001) verified the solution of the compressible Euler system does not obey the generalized Huygens’ principle due to the damped mechanism. In this paper, we proved that both of two densities and two momentums for the two-phase fluid model obey the generalized Huygens’ principle as that in Liu and Wang (Commun Math Phys 196:145–173, 1998). The main contribution is to overcome the difficulty of the non-conservation arising from the damped mechanism of the system. As a byproduct, we also extended-estimate in Wu et al. (SIAM J Math Anal 52(6):5748–5774, 2020) to-estimate with.