论文标题
在具有拖动术语的可压缩Navier-Stokes-Korteweg方程的指数衰减上
On the Exponential decay for Compressible Navier-Stokes-Korteweg equations with a Drag Term
论文作者
论文摘要
在本文中，我们将全局弱解决方案考虑到具有密度依赖性粘度的可填充的Navier-Stokes-korteweg方程，在周期性域中$ω= \ Mathbb t^3 $，相对于速度，线性拖放项。主要结果涉及使用Log-Sobolev类型不等式对此类溶液的指数衰减。为了证明这种结果，起点是D. Bresch，A。Vasseur和C. Yu [12]中引入的全局弱 - 渗透解决方案定义。假设当密度接近真空以及密度趋于无穷大时，假设剪切粘度有额外的假设，那么我们将指数衰减达到平衡。请注意，我们的结果涵盖了带有拖动项的量子Navier-Stokes系统。
In this paper, we consider global weak solutions to com-pressible Navier-Stokes-Korteweg equations with density dependent viscosities , in a periodic domain $Ω= \mathbb T^3$, with a linear drag term with respect to the velocity. The main result concerns the exponential decay to equilibrium of such solutions using log-sobolev type inequalities. In order to show such a result, the starting point is a global weak-entropy solutions definition introduced in D. Bresch, A. Vasseur and C. Yu [12]. Assuming extra assumptions on the shear viscosity when the density is close to vacuum and when the density tends to infinity, we conclude the exponential decay to equilibrium. Note that our result covers the quantum Navier-Stokes system with a drag term.
