Kinetic equations: fluid dynamical limits and viscous heating

Claude Bardos C David Levermore Seiji Ukai Tong Yang

Fluid Dynamics and Shock Waves mathscidoc:1912.43967

BULLETIN-INSTITUTE OF MATHEMATICS ACADEMIA SINICA, 3, (1), 1, 2008.3
In the long-time scale, we consider the fluid dynamical limits for the kinetic equations when the fluctuation is decomposed into even and odd parts with respect to the microscopic velocity with different scalings. It is shown that when the background state is an absolute Maxwellian, the limit fluid dynamical equations are the incompressible Navier-Stokes equations with viscous heating. This is different from the case when the even and odd parts of the fluctuation have the same scaling where the standard incompressible Navier-Stokes equations without viscous heating are obtained. On the other hand, when the background is a local Maxwellian, it is shown that the above even-odd decomposition leads to a non-classical fluid dynamical system without viscous heating which has been used to describe the ghost effect in the kinetic theory. In addition, the above even-odd decomposition is justified rigorously for the Boltzmann equation for the former case when the background is an absolute Maxwellian.
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@inproceedings{claude2008kinetic,
  title={Kinetic equations: fluid dynamical limits and viscous heating},
  author={Claude Bardos, C David Levermore, Seiji Ukai, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210949787575531},
  booktitle={BULLETIN-INSTITUTE OF MATHEMATICS ACADEMIA SINICA},
  volume={3},
  number={1},
  pages={1},
  year={2008},
}
Claude Bardos, C David Levermore, Seiji Ukai, and Tong Yang. Kinetic equations: fluid dynamical limits and viscous heating. 2008. Vol. 3. In BULLETIN-INSTITUTE OF MATHEMATICS ACADEMIA SINICA. pp.1. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210949787575531.
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