标题： 全局经典解和两相流模型的长时间行为 显示英文标题

标题： Global classical solutions and large-time behavior of the two-phase fluid model

摘要： 我们研究由可压缩等温欧拉方程与通过阻力强迫项耦合的可压缩等熵纳维-斯托克斯方程组成的两相流系统的唯一强解的全局存在性及其长时间行为。耦合系统可以作为具有强局部对齐力的Vlasov-Fokker-Planck/等熵纳维-斯托克斯方程的流体动力学极限推导出来。当初始数据足够小且光滑时，我们在扰动框架中建立了$H^s$-解的唯一存在性。我们还提供了经典解的长时间行为，显示了两个流体速度随时间演变得出的指数快速对齐。为此，我们构造了一个Lyapunov函数，用于衡量动量和质量与其平均量的波动。 显示英文摘要

摘要： We study the global existence of a unique strong solution and its large-time behavior of a two-phase fluid system consisting of the compressible isothermal Euler equations coupled with compressible isentropic Navier-Stokes equations through a drag forcing term. The coupled system can be derived as the hydrodynamic limit of the Vlasov-Fokker-Planck/isentropic Navier-Stokes equations with strong local alignment forces. When the initial data is sufficiently small and regular, we establish the unique existence of the global $H^s$-solutions in a perturbation framework. We also provide the large-time behavior of classical solutions showing the alignment between two fluid velocities exponentially fast as time evolves. For this, we construct a Lyapunov function measuring the fluctuations of momentum and mass from its averaged quantities.