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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，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κ趋于0时，此光滑解以κ7/8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[1，2]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 |
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ZHANG Si-na,ZHENG Li-yun,CHEN Zheng-zheng
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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 κ7/8 as the heat conductivity κ tends to zero. Here the strength of the contact discontinuity has no need to be small, which improves the main results in [1, 2]. |
| Key words: compressible Navier-Stokes equations convergence rate contact discontinuity |
