Zero-Viscosity Limit of the Linearized Compressible Navier-Stokes Equations with Highly Oscillatory Forces in the Half-Plane
Zero-Viscosity Limit of the Linearized Compressible Navier-Stokes Equations with Highly Oscillatory Forces in the Half-Plane
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DOI：
10.1137/040614967
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
Ya-Guang Wang;Z. Xin
中科院分区：
文献类型：
--
作者：
Ya-Guang Wang;Z. Xin
研究了半平面上具有高振荡力的线性化可压缩Navier-Stokes方程在小粘性无滑移边界条件下解的渐近行为。假设振荡波长与粘度的平方根成正比。通过渐近分析，我们得出解的主要轮廓有四项：第一项是满足线性化Euler方程的流出流，第二项是沿与线性化Euler算子的边界相切的特征场传播的振荡波，第三项是满足线性化Prandtl方程的边界层，第四项表示在边界层中传播的振荡，它由Poisson-Prandtl耦合系统的初边值问题来描述。利用能量法和模式分析方法，我们得到了该Poisson-Prandtl耦合问题的适定性，并且证明了该问题的解的存在性。
We study the asymptotic behavior of the solution to the linearized compressible Navier--Stokes equations with highly oscillatory forces in the half-plane with nonslip boundary conditions for small viscosity. The wavelength of oscillation is assumed to be proportional to the square root of the viscosity. By means of asymptotic analysis, we deduce that the leading profiles of the solution have four terms: the first one is the outflow satisfying the linearized Euler equations, the second one is an oscillatory wave propagated along the characteristic field tangential to the boundary associated with the linearized Euler operator in the half-plane, the third one is a boundary layer satisfying a linearized Prandtl equation, the fourth one represents the oscillation propagated in the boundary layer, and it is described by an initial-boundary value problem for an Poisson--Prandtl coupled system. By using the energy method and mode analysis, we obtain the well-posedness of this Poisson--Prandtl coupled problem, and...