Science-advisor
REGISTER info/FAQ
Login
username
password
     
forgot password?
register here
 
Research articles
  search articles
  reviews guidelines
  reviews
  articles index
My Pages
my alerts
  my messages
  my reviews
  my favorites
 
 
Stat
Members: 3652
Articles: 2'545'386
Articles rated: 2609

24 June 2024
 
  » arxiv » 2302.00139

 Article overview



Exploring numerical blow-up phenomena for the Keller-Segel-Navier-Stokes equations
Jesús Bonilla ; Juan Vicente Gutiérrez-Santacreu ;
Date 1 Feb 2023
AbstractThe Keller-Segel-Navier-Stokes system governs chemotaxis in liquid environments. This system is to be solved for the organism and chemoattractant densities and for the fluid velocity and pressure. It is known that if the total initial cell density mass is below $2pi$ there exist globally defined generalised solutions, but what is less understood is whether there are blow-up solutions beyond such a threshold and its optimality.
Motivated by this issue, a numerical blow-up scenario is investigated. Approximate solutions computed via a stabilised finite element method founded on a shock capturing technique are such that they satisfy emph{a priori} bounds as well as lower and $L^1(Omega)$ bounds for the cell and chemoattractant densities. In particular, this latter properties are essential in detecting numerical blow-up configurations, since the non-satisfaction of these two requirements might trigger numerical oscillations leading to non-realistic finite-time collapses into persistent Dirac-type measures.
Our findings show that the existence threshold value $2pi$ encountered for the cell density mass may not be optimal and hence it is conjectured that the critical threshold value $4pi$ may be inherited from the fluid-free Keller-Segel equations. Additionally it is observed that the formation of singular points can be neglected if the fluid flow is intensified.
Source arXiv, 2302.00139
Services Forum | Review | PDF | Favorites   
 
Visitor rating: did you like this article? no 1   2   3   4   5   yes

No review found.
 Did you like this article?

This article or document is ...
important:
of broad interest:
readable:
new:
correct:
Global appreciation:

  Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.






ScienXe.org
» my Online CV
» Free

home  |  contact  |  terms of use  |  sitemap
Copyright © 2005-2024 - Scimetrica