In this paper, we consider a compressible–incompressible two-velocity hydrodynamic system studied by Bresch et al (2015 J. Math. Pure Appl. 104 762–800) and Lions (1996 Mathematical Topics in Fluid Mechanics (Oxford: OUP)). When the density ρ is a small perturbation of a constant, we establish a priori estimates by using some delicate structure of the nonlinear terms and Hardy space. By using these a priori estimates, we prove the existence of global strong solutions and weak solutions. Our results do not require any constraint between the viscosity and the conductivity and improve the results of Bresch et al (2015) and Lions (1996) in the two-dimensional case. As an application of our results we also establish global strong solutions and weak solutions for a model of gaseous mixture and the ghost effect system.

在本文中，我们考虑了 Bresch等人(2015 J. Math. Pure Appl. 104 762–800) 和 Lions (1996流体力学数学主题(Oxford: OUP))研究的可压缩-不可压缩双速流体动力系统。当密度ρ是一个常数的小扰动时，我们通过使用非线性项和哈代空间的一些微妙结构来建立先验估计。通过使用这些先验估计，我们证明了全局强解和弱解的存在。我们的结果不需要粘度和电导率之间的任何约束，并改进了 Bresch等人的结果(2015) 和 Lions (1996) 在二维情况下。作为我们结果的应用，我们还为气体混合物和鬼效应系统模型建立了全局强解和弱解。