论文标题
多组分模型的Euler-Navier-Stokes-Korteweg方程的高摩擦极限
High friction limits of Euler-Navier-Stokes-Korteweg equations for multicomponent models
论文作者
论文摘要
在本文中，我们分析了多组分系统的Navier Stokes Korteweg方程的高摩擦状态。根据混合和摩擦项的形状，我们应执行两个限制：朝向限制密度和barycentric速度的平衡系统的高摩擦极限，以及在适当的时间缩放之后，对于极限密度的抛物线扩散，朝抛物线的梯度，梯度流动方程的扩散放松。这些限制的严格理由是通过相对熵技术在弱的，有限的能量解决方案的框架中完成的，这是在放松模型的弱，有限的能量解决方案中，根据漂移速度的扩大配方重写，朝着相应的平衡动力学的平滑解决方案。最后，由于我们的估计值对于小粘度是均匀的，因此结果对于Euler Korteweg多组分模型也有效，并且可以通过将粘度发送到零来获得相应的估计。
In this paper we analyze the high friction regime for the Navier Stokes Korteweg equations for multicomponent systems. According to the shape of the mixing and friction terms, we shall perform two limits: the high friction limit toward an equilibrium system for the limit densities and the barycentric velocity, and, after an appropriate time scaling, the diffusive relaxation toward parabolic, gradient flow equations for the limit densities. The rigorous justification of these limits is done by means of relative entropy techniques in the framework of weak, finite energy solutions of the relaxation models, rewritten in the enlarged formulation in terms of the drift velocity, toward smooth solutions of the corresponding equilibrium dynamics. Finally, since our estimates are uniform for small viscosity, the results are also valid for the Euler Korteweg multicomponent models, and the corresponding estimates can be obtained by sending the viscosity to zero.
