论文标题
关于整个空间中无压力的Euler-Navier-Stokes系统的Cauchy问题
On the Cauchy problem for the pressureless Euler-Navier-Stokes system in the whole space
论文作者
论文摘要
在本文中，我们研究了由无压力Euler方程组成的两相流体模型和不可压缩的Navier-Stokes方程组成的全球库奇问题，在这些模型中，两个方程的耦合是通过阻力。当初始数据足够小且规则时，我们为该系统建立了全球及时的存在和经典解决方案的独特性。在没有压力的情况下，出现主要困难。为了解决它，我们正确地结合了经典解决方案的大型行为和引导参数，以构建全球范围内独特的经典解决方案。
In this paper, we study the global Cauchy problem for a two-phase fluid model consisting of the pressureless Euler equations and the incompressible Navier-Stokes equations where the coupling of two equations is through the drag force. We establish the global-in-time existence and uniqueness of classical solutions for that system when the initial data are sufficiently small and regular. Main difficulties arise in the absence of pressure in the Euler equations. In order to resolve it, we properly combine the large-time behavior of classical solutions and the bootstrapping argument to construct the global-in-time unique classical solutions.
