Incompressible limit for compressible viscoelastic flows with large velocity
Incompressible limit for compressible viscoelastic flows with large velocity
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DOI：
10.1515/anona-2022-0324
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发表时间：
2023-01
影响因子：
4.2
通讯作者：
Xianpeng Hu;Yaobin Ou;Dehua Wang;Lu Yang
中科院分区：
文献类型：
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作者：
Xianpeng Hu;Yaobin Ou;Dehua Wang;Lu Yang
摘要我们讨论了三维可压缩粘弹性方程具有任意大初速的整体时间强解的不可压缩极限。与低马赫数极限不同，体积粘度的较大值实现了不可压缩性。为了得到一致的估计，我们建立了速度的势能部分和无散度部分的估计。当体积粘性趋于无穷大时，与压力波相关的色散趋于消失，但大体积粘性对速度的势能部分提供了强烈的耗散，迫使流动几乎不可压缩。
Abstract We are concerned with the incompressible limit of global-in-time strong solutions with arbitrary large initial velocity for the three-dimensional compressible viscoelastic equations. The incompressibility is achieved by the large value of the volume viscosity, which is different from the low Mach number limit. To obtain the uniform estimates, we establish the estimates for the potential part and the divergence-free part of the velocity. As the volume viscosity goes to infinity, the dispersion associated with the pressure waves tends to disappear, but the large volume viscosity provides a strong dissipation on the potential part of the velocity forcing the flow to be almost incompressible.