Inviscid limits for the Navier–Stokes equations with Navier friction boundary conditions
Inviscid limits for the Navier–Stokes equations with Navier friction boundary conditions
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DOI：
10.1088/0951-7715/19/4/007
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发表时间：
2006-04
期刊：
影响因子：
1.7
通讯作者：
D. Iftimie;G. Planas
中科院分区：
文献类型：
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作者：
D. Iftimie;G. Planas
我们考虑了具有Navier摩擦边界条件的Navier-Stokes方程，并证明了两个结果。首先，在有界域的情况下，我们证明了当粘性趋于0时，欧拉方程的弱勒雷解(在⩾3的时间局部收敛，在2维的时间全局收敛)收敛到欧拉方程的强解，只要初始数据在L2收敛到足够光滑的极限。其次，我们考虑了半空间和各向异性粘性的情形：我们固定水平粘性，将垂直粘性发送到0，并且在对初始数据较弱的假设下证明了收敛到期望的极限系统。
We consider the Navier–Stokes equations with Navier friction boundary conditions and prove two results. First, in the case of a bounded domain we prove that weak Leray solutions converge (locally in time in dimension ⩾3 and globally in time in dimension 2) as the viscosity goes to 0 to a strong solution of the Euler equations, provided that the initial data converge in L2 to a sufficiently smooth limit. Second, we consider the case of a half-space and anisotropic viscosities: we fix the horizontal viscosity, send the vertical viscosity to 0 and prove convergence to the expected limit system under a weaker hypothesis on the initial data.