A characterization of probability measure with finite moment and an application to the Boltzmann equation

Yong-Kum Cho Yoshinori Morimoto Shuaikun Wang Tong Yang

Analysis of PDEs mathscidoc:1912.431017

arXiv preprint arXiv:1512.00629, 2015.12
We characterize probability measure with finite moment of any order in terms of the symmetric difference operators of their Fourier transforms. By using our new characterization, we prove the continuity f (t, v)\in C ((0,\infty), L^ 1_ {2k-2+ }) , where f (t, v)\in C ((0,\infty), L^ 1_ {2k-2+ }) stands for the density of unique measure-valued solution f (t, v)\in C ((0,\infty), L^ 1_ {2k-2+ }) of the Cauchy problem for the homogeneous non-cutoff Boltzmann equation, with Maxwellian molecules, corresponding to a probability measure initial datum f (t, v)\in C ((0,\infty), L^ 1_ {2k-2+ }) satisfying\[\int| v|^{2k-2+ } dF_0 (v)<\infty, 0\leq < 2, k= 2, 3, 4,\cdots\] provided that f (t, v)\in C ((0,\infty), L^ 1_ {2k-2+ }) is not a single Dirac mass.
No keywords uploaded!
[ Download ] [ 2019-12-24 21:12:35 uploaded by Tong_Yang ] [ 215 downloads ] [ 0 comments ]
@inproceedings{yong-kum2015a,
  title={A characterization of probability measure with finite moment and an application to the Boltzmann equation},
  author={Yong-Kum Cho, Yoshinori Morimoto, Shuaikun Wang, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211235955219581},
  booktitle={arXiv preprint arXiv:1512.00629},
  year={2015},
}
Yong-Kum Cho, Yoshinori Morimoto, Shuaikun Wang, and Tong Yang. A characterization of probability measure with finite moment and an application to the Boltzmann equation. 2015. In arXiv preprint arXiv:1512.00629. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211235955219581.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved