Well/Ill-Posedness of the Boltzmann Equation with Soft Potential

被引：0

作者：

Chen, Xuwen ^{[1
]}

Shen, Shunlin ^{[2
]}

Zhang, Zhifei ^{[3
]}

机构：

[1] Univ Rochester, Dept Math, Rochester, NY 14627 USA

[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

[3] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2024年 / 405卷 / 12期

关键词：

NONLINEAR SCHRODINGER-EQUATION; GROSS-PITAEVSKII HIERARCHY; ILL-POSEDNESS; RIGOROUS DERIVATION; CLASSICAL-SOLUTIONS; LOCAL EXISTENCE; QUANTUM; REGULARITY; SPACE; UNIQUENESS;

D O I：

10.1007/s00220-024-05157-6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the Boltzmann equation with the soft potential and angular cutoff. Inspired by the methods from dispersive PDEs, we establish its sharp local well-posedness and ill-posedness in Hs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H<^>{s}$$\end{document} Sobolev space. We find the well/ill-posedness separation at regularity s=d-12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s=\frac{d-1}{2}$$\end{document}, strictly 12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{1}{2}$$\end{document}-derivative higher than the scaling-invariant index s=d-22\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$s=\frac{d-2}{2}$$\end{document}, the usually expected separation point.

引用

页数：51

共 65 条

[61] Exponential decay for soft potentials near Maxwellian [J].