Stability of Compressible Vortex Sheets in Steady Supersonic Euler Flows over Lipschitz Walls
Stability of Compressible Vortex Sheets in Steady Supersonic Euler Flows over Lipschitz Walls
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DOI：
10.1137/050642976
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发表时间：
2007-02
期刊：
影响因子：
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通讯作者：
Gui-Qiang G. Chen;Yongqian Zhang;Dianwen Zhu
中科院分区：
文献类型：
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作者：
Gui-Qiang G. Chen;Yongqian Zhang;Dianwen Zhu
我们关心 $BV$ 边界扰动下 Lipschitz 壁上二维稳定超音速欧拉流中可压缩涡片的稳定性，因为稳定超音速欧拉流在许多物理情况下都很重要。事实证明，即使在 Lipschitz 壁的 $BV$ 扰动下，超声速流中的稳定可压缩涡片在结构上也是全局稳定的。为了实现这一目标，我们开发了一种改进的 Glimm 差分方案，并通过自然地合并 Lipschitz 边界和强涡片，并通过跟踪边界波和弱波之间以及强涡片和弱波之间的相互作用，确定了 Glimm 型泛函以获得所需的 $BV$ 估计。然后，使用这些估计来建立全局熵解的近似解和熵解的强可压缩涡旋片的相应近似强涡旋片的收敛。不对称...
We are concerned with the stability of compressible vortex sheets in two‐dimensional steady supersonic Euler flows over Lipschitz walls under a $BV$ boundary perturbation, since steady supersonic Euler flows are important in many physical situations. It is proved that steady compressible vortex sheets in supersonic flow are stable in structure globally, even under the $BV$ perturbation of the Lipschitz walls. In order to achieve this, we develop a modified Glimm difference scheme and identify a Glimm‐type functional to obtain the required $BV$ estimates by incorporating the Lipschitz boundary and the strong vortex sheets naturally and by tracing the interaction not only between the boundary and weak waves but also between the strong vortex sheets and weak waves. Then these estimates are employed to establish the convergence of the approximate solutions to a global entropy solution and the corresponding approximate strong vortex sheets to a strong compressible vortex sheet of the entropy solution. The asym...