| 谢玲玲,卞新想.2维可压缩Navier-Stokes方程带真空平坦稀疏波粘性消失极限[J].数学年刊A辑,2026,(1):85~112 |
| 2维可压缩Navier-Stokes方程带真空平坦稀疏波粘性消失极限 |
| Vanishing Viscosity Limit to Planar Rarefaction Wave with Vacuum for 2D Compressible Navier-Stokes Equations |
| 投稿时间：2024-12-23 修订日期：2026-03-02 |
| DOI：10.16205/j.cnki.cama.2026.0008 |
| 中文关键词: 可压缩Navier-Stokes方程 平坦稀疏波 真空 粘性消失极限 |
| 英文关键词:Compressible Navier-Stokes equations Planar rarefaction wave Vacuum Vanishing viscosity limit |
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| 中文摘要: |
| 主要研究2维等熵可压缩Navier-Stokes方程带真空平坦稀疏波的粘性消失极限. 得到了关于粘性系数的一致收敛率. 主要创新和难点在于如何处理由高维稀疏波真空状态所引起的退化. 在真空附近利用适当截断和尺度伸缩技巧来处理真空引起的奇性问题. 最终, 通过引入截断参数和处理2维可压缩Navier-Stokes方程的粘性误差项, 得到了稀疏波真空附近的无粘性衰减率. 证明过程基于基本能量法. |
| 英文摘要: |
| This paper mainly studies the vanishing viscosity limit of planar rarefaction wave with vacuum for the two-dimensional (2D for short) isentropic compressible Navier-Stokes equations. A uniform convergence rate related to the viscosity coefficients is obtained. The main novelty and difficulty lie in controlling the degeneracy caused by vacuum states of the rarefaction wave in the multidimensional setting. Appropriate cut-off and scaling techniques are applied near the vacuum states. Eventually, the authors obtain the inviscid decay rate around the planar rarefaction wave with vacuum by introducing the cut-off parameter and handling the viscous error terms of the two-dimensional compressible Navier-Stokes equations. The proof is based on the elementary energy method. |
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