Vanishing dissipation limit to the planar rarefaction wave for the three-dimensional compressible Navier-Stokes-Fourier equations
Vanishing dissipation limit to the planar rarefaction wave for the three-dimensional compressible Navier-Stokes-Fourier equations
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DOI：
10.1016/j.jfa.2022.109499
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发表时间：
2021-01
影响因子：
1.7
通讯作者：
Lin-an Li;Dehua Wang;Yi Wang
中科院分区：
文献类型：
--
作者：
Lin-an Li;Dehua Wang;Yi Wang
研究了三维可压缩Navier-Stokes-Fourier方程到相应的三维全Euler方程的耗散消失极限。我们的结果是双重的。首先，我们证明了三维可压缩Navier-Stokes-Fourier方程组存在一族光滑解，该光滑解收敛于具有任意强度的三维可压缩Euler方程组的平面稀疏波解。其次，我们得到了一致的收敛速度的粘性和导热系数。由于3D设置，二维情况下的方法不能直接应用。相反，3D情况的分析是在原始的非标度变量中进行的，因此耗散项更加奇异。新的思想和技术的发展，以建立统一的估计。对于稳定性分析来说，需要对耗散系数进行更精确的优先假设，而对于通量项的物理结构的抵消，一些新的观测结果基本上被用来证明三维极限的合理性。此外，我们发现，相对于耗散系数的衰减率是由非线性通量项的原始变量的3D极限。
We study the vanishing dissipation limit of the three-dimensional (3D) compressible Navier-Stokes-Fourier equations to the corresponding 3D full Euler equations. Our results are twofold. First, we prove that the 3D compressible Navier-Stokes-Fourier equations admit a family of smooth solutions that converge to the planar rarefaction wave solution of the 3D compressible Euler equations with arbitrary strength. Second, we obtain a uniform convergence rate in terms of the viscosity and heat-conductivity coefficients. Due to the 3D setting the approach for the two-dimensional case could not be applied directly. Instead, the analysis of the 3D case is carried out in the original non-scaled variables, and consequently the dissipation terms are more singular. Novel ideas and techniques are developed to establish the uniform estimates. More accuratea prioriassumptions with respect to the dissipation coefficients are crucially needed for the stability analysis, and some new observations on the cancellations of the physical structures for the flux terms are essentially used to justify the 3D limit. Moreover, we find that the decay rate with respect to the dissipation coefficients is determined by the nonlinear flux terms in the original variables for the 3D limit.