A new characterization and global regularity of infinite energy solutions to the homogeneous Boltzmann equation

Yoshinori Morimoto; Shuaikun Wang; Tong Yang

doi:10.1016/j.matpur.2014.09.002

Author(s)

Yoshinori Morimoto
Shuaikun Wang
Tong Yang

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Pages (from-to)	809-829
Journal / Publication	Journal de Mathématiques Pures et Appliquées
Volume	103
Issue number	3
Online published	29 Oct 2014
Publication status	Published - Mar 2015

Link(s)

DOI	DOI https://doi.org/10.1016/j.matpur.2014.09.002 Final Published version
	Check@CityULib
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-84922844669&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(156ce21c-409a-461c-bd4a-58bf6cc6a691).html

Abstract

The purpose of this paper is to introduce a new characterization of the characteristic functions for the study on the measure valued solution to the homogeneous Boltzmann equation so that it precisely captures the moment constraint in physics. This significantly improves the previous result by Cannone and Karch (2010) [2] in the sense that the new characterization gives a complete description of infinite energy solutions for the Maxwellian cross section. In addition, the global in time smoothing effect of the infinite energy solution is justified as for the finite energy solution except for a single Dirac mass initial datum.

Research Area(s)

Boltzmann equation, Infinite energy solution, Maxwellian molecule, Smoothing effect

Citation Format(s)

[ RIS ] [ BibTeX ]

A new characterization and global regularity of infinite energy solutions to the homogeneous Boltzmann equation. / Morimoto, Yoshinori; Wang, Shuaikun; Yang, Tong.

In: Journal de Mathématiques Pures et Appliquées, Vol. 103, No. 3, 03.2015, p. 809-829.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review

Morimoto, Y, Wang, S & Yang, T 2015, 'A new characterization and global regularity of infinite energy solutions to the homogeneous Boltzmann equation', Journal de Mathématiques Pures et Appliquées, vol. 103, no. 3, pp. 809-829. https://doi.org/10.1016/j.matpur.2014.09.002

Morimoto, Y., Wang, S., & Yang, T. (2015). A new characterization and global regularity of infinite energy solutions to the homogeneous Boltzmann equation. Journal de Mathématiques Pures et Appliquées, 103(3), 809-829. https://doi.org/10.1016/j.matpur.2014.09.002

Morimoto Y, Wang S, Yang T. A new characterization and global regularity of infinite energy solutions to the homogeneous Boltzmann equation. Journal de Mathématiques Pures et Appliquées. 2015 Mar;103(3):809-829. Epub 2014 Oct 29. doi: 10.1016/j.matpur.2014.09.002

Morimoto, Yoshinori ; Wang, Shuaikun ; Yang, Tong. / A new characterization and global regularity of infinite energy solutions to the homogeneous Boltzmann equation. In: Journal de Mathématiques Pures et Appliquées. 2015 ; Vol. 103, No. 3. pp. 809-829.