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 \(L^2\)-estimate in Wu et al. (SIAM J Math Anal 52(6):5748–5774, 2020) to \(L^p\)-estimate with \(p>1\).

我们研究了 Choi (SIAM J Math Anal 48:3090–3122, 2016) 推导的两相流体模型柯西问题的经典解在初始数据足够小且规则时的点状时空行为。该模型是可压缩阻尼欧拉系统通过阻力与可压缩奈弗-斯托克斯系统耦合。众所周知，Liu 和 Wang (Commun Math Phys 196:145–173, 1998) 验证了可压缩 Naiver-Stokes 系统的解遵循广义惠更斯原理，而 Wang 和 Yang (J Differ Equ 173:410–450 , 2001）验证了可压缩欧拉系统的解由于阻尼机制而不遵循广义惠更斯原理。在本文中，我们证明了两相流体模型的两个密度和两个动量都遵循刘和王的广义惠更斯原理（Commun Math Phys 196:145–173, 1998）。主要贡献是克服了系统阻尼机制带来的不守恒困难。作为副产品，我们还扩展了Wu 等人的\(L^2\)估计。 (SIAM J Math Anal 52(6):5748–5774, 2020) 到\(L^p\) -用\(p>1\)估计。