Blowup of solutions for a transport equation with nonlocal velocity and damping-Reference-Cited by-同舟云学术

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Blowup of solutions for a transport equation with nonlocal velocity and damping

Published:2023-09-01 Issue:9 Volume:64 Page:
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:

Author:

Li You¹,Liu Yannan²^ORCID,Zhang Wanwan³^ORCID

Affiliation:

1. School of Mathematical and Computational Science, Xiangtan University 1 , Hunan 411105, People’s Republic of China

2. Department of Mathematics, Beijing Technology and Business University 2 , Beijing 100048, People’s Republic of China

3. School of Mathematics and Statistics, Jiangxi Normal University 3 , Nanchang 330022, Jiangxi, People’s Republic of China

Abstract

We study a transport equation with nonlocal velocity and power law type damping. We show that a certain class of initial data smooth solution blows up in finite time.

Funder

National Natural Science Foundation of China

Natural Science Foundation of Beijing Municipality

China Postdoctoral Science Foundation

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://pubs.aip.org/aip/jmp/article-pdf/doi/10.1063/5.0140037/18120895/091503_1_5.0140037.pdf

Reference32 articles.

1. On the blow up of a non-local transport equation in compact manifolds;Proc. Am. Math. Soc.,2023

2. An inequality for Riesz transforms implying blow-up for some nonlinear and nonlocal transport equations;Adv. Math.,2007

3. Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation;Ann. Math.,2010

4. Generalized surface quasi-geostrophic equations with singular velocities;Commun. Pure Appl. Math.,2012

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