Open AccessWell-posedness and critical thresholds in a nonlocal Euler system with relaxation
Author(s) -
Manas Bhatnagar,
Hailiang Liu
Publication year - 2021
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021076
Subject(s) - euler system , uniqueness , limit (mathematics) , relaxation (psychology) , dimension (graph theory) , euler equations , euler's formula , mathematics , class (philosophy) , mathematical analysis , scaling , pure mathematics , physics , computer science , geometry , psychology , social psychology , artificial intelligence
We propose and study a nonlocal Euler system with relaxation, which tends to a strictly hyperbolic system under the hyperbolic scaling limit. An independent proof of the local existence and uniqueness of this system is presented in any spatial dimension. We further derive a precise critical threshold for this system in one dimensional setting. Our result reveals that such nonlocal system admits global smooth solutions for a large class of initial data. Thus, the nonlocal velocity regularizes the generic finite-time breakdown in the pressureless Euler system.