Non-existence of some approximately self-similar singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann equations-Reference-Cited by-同舟云学术

Non-existence of some approximately self-similar singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann equations

Published:2021-12-23 Issue:3 Volume:375 Page:2187-2216
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Bedrossian Jacob,Gualdani Maria,Snelson Stanley

Abstract

We consider the homogeneous and inhomogeneous Landau equation for very soft and Coulomb potentials and show that approximate Type I self-similar blow-up solutions do not exist under mild decay assumptions on the profile. We extend our analysis to the Vlasov-Poisson-Landau system and to the Boltzmann equation without angular cut-off.

Funder

National Science Foundation

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/tran/2022-375-03/S0002-9947-2021-08568-2/tran8568_AM.pdf

Reference74 articles.

1. Entropy dissipation and long-range interactions;Alexandre, R.;Arch. Ration. Mech. Anal.,2000

2. Regularizing effect and local existence for the non-cutoff Boltzmann equation;Alexandre, Radjesvarane;Arch. Ration. Mech. Anal.,2010

3. Bounded solutions of the Boltzmann equation in the whole space;Alexandre, Radjesvarane;Kinet. Relat. Models,2011

4. On the Landau approximation in plasma physics;Alexandre, R.;Ann. Inst. H. Poincar\'{e} Anal. Non Lin\'{e}aire,2004

5. The existence of a generalized solution of Landau’s equation;Arsen′ev, A. A.;\v{Z}. Vy\v{c}isl. Mat i Mat. Fiz.,1977

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Local-In-Time Strong Solutions of the Homogeneous Landau–Coulomb Equation with $$L^p$$ Initial Datum;La Matematica;2024-02-26