流体力学中强迫振荡波相互作用耗散的产生
On the Production of Dissipation by Interaction of Forced Oscillating Waves in Fluid Dynamics
摘要：
在二维Navier-Stokes模型的背景下，我们给出了一族定义在不依赖于$ε\in]0,1]$的带$[0,T]\times\R^2$上的精确振荡解$\{u_ε\}_ε$.精确的解决方案是描述由于一个完整的扩展，揭示了边界层的时间$t=0$。各种尺度（1、$1/ε$和$1/ε^2$）的相互作用产生了通过添加扩散而给出的宏观效应。为了证明$\{u_ε\}_ε$的存在性，我们需要执行各种Sobolev估计，这些估计依赖于来自方程的双曲和抛物线部分的信息之间的精确平衡。
英文摘要：
In the context of some bidimensionnal Navier-Stokes model, we exhibit a family of exact oscillating solutions $\{u_ε\}_ε$ defined on some strip $[0,T]\times\R^2$ which does not depend on $ε\in]0,1]$. The exact solutions is described thanks to a complete expansions which reveal a boundary layer in time $t=0$. The interactions of the various scales (1, $1/ε$ and $1/ε^2$) produce a macroscopic effect given by the addition of a diffusion. To justify the existence of $\{u_ε\}_ε$, we need to perform various Sobolev estimates that rely on a refined balance between the informations coming from the hyperbolic and parabolic parts of the equations.
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