Topics in Kinetic Theory

In this short course, I will introduce our works on the singular behaviour of a rarefied gas on a convex body and on kinetic modeling for phase transition. The first topic will be discussed through a study of a rarefied gas flow around a rotating sphere and the second topic will be discussed through a minimum kinetic model for the phase transition. For the second topic, the fluid-dynamic limit that leads to the Cahn-Hilliard type equation will be discussed as well.

References:

[1] S. Taguchi, K. Saito, and S. Takata, J. Fluid Mech. 862, 5-33 (2019); https://doi.org/10.1017/jfm.2018.946.

[2] S. Takata and S. Taguchi, J. Stat. Phys. 168, 1319-1352 (2017); https://doi.org/10.1007/s10955-017-1850-7.

[3] S. Takata and T. Noguchi, J. Stat. Phys. 172, 880-903 (2018); https://doi.org/10.1007/s10955-018-2068-z.

[4] S. Takata, T. Matsumoto, A. Hirahara, and M. Hattori, Phys. Rev. E 98, 052123 (2018); https://doi.org/10.1103/physRevE.98.052123.

[5] S. Takata, T. Matsumoto, and M. Hattori, Phys. Rev. E 103, 062110 (2021); https://link.aps.org/doi/10.1103/PhysRevE.103.062110