A combination of energy method and spectral analysis for study of equations of gas motion

Renjun Duan Seiji Ukai Tong Yang

Analysis of PDEs mathscidoc:1912.43978

Frontiers of Mathematics in China, 4, (2), 253-282, 2009.6
There have been extensive studies on the large time behavior of solutions to systems on gas motions, such as the Navier-Stokes equations and the Boltzmann equation. Recently, an approach is introduced by combining the energy method and the spectral analysis to the study of the optimal rates of convergence to the asymptotic profiles. In this paper, we will first illustrate this method by using some simple model and then we will present some recent results on the Navier-Stokes equations and the Boltzmann equation. Precisely, we prove the stability of the non-trivial steady state for the Navier-Stokes equations with potential forces and also obtain the optimal rate of convergence of solutions toward the steady state. The same issue was also studied for the Boltzmann equation in the presence of the general time-space dependent forces. It is expected that this approach can also be applied to other dissipative
No keywords uploaded!
[ Download ] [ 2019-12-24 21:10:25 uploaded by Tong_Yang ] [ 236 downloads ] [ 0 comments ]
@inproceedings{renjun2009a,
  title={A combination of energy method and spectral analysis for study of equations of gas motion},
  author={Renjun Duan, Seiji Ukai, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211025210772542},
  booktitle={Frontiers of Mathematics in China},
  volume={4},
  number={2},
  pages={253-282},
  year={2009},
}
Renjun Duan, Seiji Ukai, and Tong Yang. A combination of energy method and spectral analysis for study of equations of gas motion. 2009. Vol. 4. In Frontiers of Mathematics in China. pp.253-282. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211025210772542.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved