Semantic Scholar Open Access 2009 39 sitasi

Distributional and Classical Solutions to the Cauchy Boltzmann Problem for Soft Potentials with Integrable Angular Cross Section

R. Alonso I. Gamba

Lihat Sumber DOI

Abstrak

This paper focuses on the study of existence and uniqueness of distributional and classical solutions to the Cauchy Boltzmann problem for the soft potential case assuming Sn−1 integrability of the angular part of the collision kernel (Grad cut-off assumption). For this purpose we revisit the Kaniel–Shinbrot iteration technique to present an elementary proof of existence and uniqueness results that includes the large data near local Maxwellian regime with possibly infinite initial mass. We study the propagation of regularity using a recent estimate for the positive collision operator given in (Alonso et al. in Convolution inequalities for the Boltzmann collision operator. arXiv:0902.0507 [math.AP]) , by E. Carneiro and the authors, that allows us to show such propagation without additional conditions on the collision kernel. Finally, an Lp-stability result (with 1≤p≤∞) is presented assuming the aforementioned condition.

Topik & Kata Kunci

Physics Mathematics

Penulis (2)

R. Alonso

I. Gamba

Format Sitasi

APA MLA BibTeX

Alonso, R., Gamba, I. (2009). Distributional and Classical Solutions to the Cauchy Boltzmann Problem for Soft Potentials with Integrable Angular Cross Section. https://doi.org/10.1007/s10955-009-9873-3

Akses Cepat

Lihat di Sumber doi.org/10.1007/s10955-009-9873-3

Informasi Jurnal

Tahun Terbit: 2009
Bahasa: en
Total Sitasi: 39×
Sumber Database: Semantic Scholar
DOI: 10.1007/s10955-009-9873-3
Akses: Open Access ✓