三维可压缩等熵Navier-Stokes方程平面疏散波在周期扰动下的渐近稳定性(黄飞敏,袁谦)

2022-12-26 | 撰稿: | 浏览:

 We study a Cauchy problem for the 3-d compressible isentropic Navier-Stokes equations, in which the initial data is a 3-d periodic perturbation around a planar rarefaction wave. We prove that the solution of the Cauchy problem exists globally in time and tends to the background rarefaction wave in the $ L^\infty(R^3) $ space as $ t\to +\infty. $ The result reveals that even though the initial perturbation has infinite oscillations at the far field and is not integrable along any direction of space, the planar rarefaction wave is nonlinearly stable for the 3-d N-S equations.

 

Publication: Advances in Mathematics 404, Paper No. 108452, 27 pp. (2022)

 

Authors:

 

Feimin Huang

Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China, and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Email: fhuang@amt.ac.cn

 

Lingda Xu

Department of Mathematics, Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China, and Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing 101408, China

Email: xulingda@tsinghua.edu.cn

 

Qian Yuan 

Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190, China

Email: qyuan@amss.ac.cn


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