多组分模型Euler-Navier-Stokes-Korteweg方程的高摩擦极限
High friction limits of Euler-Navier-Stokes-Korteweg equations for multicomponent models
摘要：
在本文中，我们分析了高摩擦制度的Navier-Stokes-Korteweg方程的多组分系统。根据混合项和摩擦项的形状，我们将实现两个极限：对于极限密度和重心速度，高摩擦极限朝向平衡系统;对于极限密度，经过适当的时间标度，扩散松弛朝向抛物线梯度流方程。严格的理由，这些限制是通过相对熵技术的弱，有限能量的解决方案的松弛模型的框架内，重写在扩大的制定方面的漂移速度，对平滑的解决方案，相应的平衡动力学。最后，由于我们的估计是一致的小粘度，结果也是有效的欧拉Korteweg多组分模型，相应的估计可以通过发送粘度为零。
英文摘要：
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.
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