Thermal creep flow for the Boltzmann equation
Feimin Huang
Chinese Annals of Mathematics, Series B ›› 2015, Vol. 36 ›› Issue (5) : 855 -870.
Thermal creep flow for the Boltzmann equation
It is known that the Boltzmann equation has close relation to the classical systems in fluid dynamics. However, it provides more information on the microscopic level so that some phenomena, like the thermal creep flow, can not be modeled by the classical systems of fluid dynamics, such as the Euler equations. The author gives an example to show this phenomenon rigorously in a special setting. This paper is completely based on the author’s recent work, jointly with Wang and Yang.
Thermal creep flow / Non-classical fluid system / Boltzmann equation
| [1] |
|
| [2] |
|
| [3] |
|
| [4] |
Boltzmann, L., Lectures on Gas Theory, translated by G. Stephen Brush, Dover Publications, New York, 1964. |
| [5] |
|
| [6] |
|
| [7] |
|
| [8] |
|
| [9] |
|
| [10] |
|
| [11] |
|
| [12] |
|
| [13] |
|
| [14] |
|
| [15] |
Grad, H., Asymptotic Theory of the Boltzmann Equation II, Rarefied Gas Dynamics, J. A. Laurmann (ed.), Vol. 1, Academic Press, New York, 1963, 26–59. |
| [16] |
|
| [17] |
|
| [18] |
|
| [19] |
|
| [20] |
Huang, F. M., Wang, Y., Wang, Y. and Yang, T., Justification of diffusion limit for the Boltzmann equation with a non-trivial profile, submitted. |
| [21] |
|
| [22] |
|
| [23] |
|
| [24] |
|
| [25] |
Levermore, C. D., Sun, W. R. and Trivisa, K., Local well-posedness of a ghost effect system, to appear. |
| [26] |
|
| [27] |
|
| [28] |
|
| [29] |
|
| [30] |
|
| [31] |
|
| [32] |
|
| [33] |
Ukai, S., Solutions of the Boltzmann Equation, Pattern and Waves-Qualitative Analysis of Nonlinear Differential Equations, M. Mimura and T. Nishida (eds.), Studies of Mathematics and Its Applications, 18, Kinokuniya-North-Holland, Tokyo, 1986, 37–96. |
| [34] |
|
| [35] |
|
| [36] |
|
| [37] |
|
/
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|
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