Propagation of regularity and finite-time collisions for the thermomechanical Cucker-Smale model with a singular communication

Young Pil Choi, Seung Yeal Ha, Jeongho Kim

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

We study dynamical behaviors of the ensemble of thermomechanical Cucker-Smale (in short TCS) particles with singular power-law communication weights in velocity and temperatures. For the particle TCS model, we present several sufficient frameworks for the global regularity of solution and a finite-time breakdown depending on the blow-up exponents in the powerlaw communication weights at the origin where the relative spatial distances become zero. More precisely, when the blow-up exponent in velocity communication weight is greater than unity and the blow-up exponent in temperature communication weights is more than twice of blow-up exponent in velocity communication, we show that there will be no finite time collision between particles, unless there are collisions initially. In contrast, when the blow-up exponent of velocity communication weight is smaller than unity, we show that there can be a collision in finite time. For the kinetic TCS equation, we present a local-in-time existence of a unique weak solution using the suitable regularization and compactness arguments.

Original languageEnglish
Pages (from-to)379-407
Number of pages29
JournalNetworks and Heterogeneous Media
Volume13
Issue number3
DOIs
Publication statusPublished - 2018 Sep 1

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Collision
Blow-up
Regularity
Propagation
Exponent
Communication
Power Law
Model
Global Regularity
Regularity of Solutions
Kinetic Equation
Dynamical Behavior
Weak Solution
Breakdown
Compactness
Regularization
Ensemble
Sufficient
Temperature
Kinetics

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Engineering(all)
  • Computer Science Applications
  • Applied Mathematics

Cite this

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Propagation of regularity and finite-time collisions for the thermomechanical Cucker-Smale model with a singular communication. / Choi, Young Pil; Ha, Seung Yeal; Kim, Jeongho.

In: Networks and Heterogeneous Media, Vol. 13, No. 3, 01.09.2018, p. 379-407.

Research output: Contribution to journalArticle

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