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摘要: |
本文研究了一维可压缩Navier-Stokes方程组趋向于接触间断波的零耗散极限问题. 利用一个新的先验假设及一些精细的能量估计, 我们证明了当可压缩Euler方程组的黎曼问题存在一个接触间断波解时, 相应的可压缩Navier-Stokes方程组存在一个整体光滑解, 并且当热传导系数$\kappa$趋于0时, 此光滑解以$\kappa^{\frac{7}{8}}$的速率趋向于接触间断波. 这里接触间断波的强度不需要小. 本文改进了文献\cite{S.-X. Ma-2012,S.-X. Ma-2010}中的主要结果. |
关键词: 可压缩Navier-Stokes方程组 收敛速率 接触间断波 |
DOI: |
分类号:O175. 29 |
基金项目:国家自然科学基金资助(11501003) |
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Zero dissipation limit to contact discontinuity for the one-dimensional compressible Navier-Stokes equations |
Zhang Sina,Chen Zhengzheng
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Abstract: |
This paper is concerned with the zero dissipation limit to contact discontinuity for the one-dimensional compressible Navier-Stokes equations. By using a new a priori assumption and some refined energy estimates, we show that when the Riemann problem of the compressible Euler equations admits a contact discontinuity solution, the corresponding Navier-Stokes equations has a unique global smooth solution, which converges to the contact discontinuity at a rate $\kappa^{\frac{7}{8}}$ as the heat conductivity $\kappa$ tends to zero. Here the strength of the contact discontinuity has no need to be small. This improves the main results in \cite{S.-X. Ma-2012,S.-X. Ma-2010}. |
Key words: Compressible Navier-Stokes equations Convergence rate Contact discontinuity. |