Abstract
The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay rate t-5/4) as t→+∞ to that of the compressible Navier-Stokes equation for the corresponding initial data.
| Original language | English |
|---|---|
| Pages (from-to) | 97-124 |
| Number of pages | 28 |
| Journal | Communications in Mathematical Physics |
| Volume | 70 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jun 1 1979 |
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All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
Cite this
On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation. / Kawashima, Shuichi; Matsumura, Akitaka; Nishida, Takaaki.
In: Communications in Mathematical Physics, Vol. 70, No. 2, 01.06.1979, p. 97-124.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation
AU - Kawashima, Shuichi
AU - Matsumura, Akitaka
AU - Nishida, Takaaki
PY - 1979/6/1
Y1 - 1979/6/1
N2 - The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay rate t-5/4) as t→+∞ to that of the compressible Navier-Stokes equation for the corresponding initial data.
AB - The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay rate t-5/4) as t→+∞ to that of the compressible Navier-Stokes equation for the corresponding initial data.
UR - http://www.scopus.com/inward/record.url?scp=0040193736&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0040193736&partnerID=8YFLogxK
U2 - 10.1007/BF01982349
DO - 10.1007/BF01982349
M3 - Article
AN - SCOPUS:0040193736
VL - 70
SP - 97
EP - 124
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 2
ER -