Finite-time blow-up phenomena of Vlasov/Navier–Stokes equations and related systems

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9 Citations (Scopus)

Abstract

This paper deals with the finite-time blow-up phenomena of classical solutions for Vlasov/Navier–Stokes equations under suitable assumptions on the initial configurations. We show that a solution to the coupled kinetic-fluid system may be initially smooth, however, it can become singular in a finite period of time. We provide a simple idea of showing the finite time blow up of classical solutions to the coupled system which has not been studied so far. We also obtain analogous results for related systems, such as isentropic compressible Navier–Stokes equations, two-phase fluid equations consisting of pressureless Euler equations and Navier–Stokes equations, and thick sprays model.

Original languageEnglish
Pages (from-to)991-1021
Number of pages31
JournalJournal des Mathematiques Pures et Appliquees
Volume108
Issue number6
DOIs
Publication statusPublished - 2017 Dec

Bibliographical note

Funding Information:
The author also thanks Professor Jos? A. Carrillo and Professor Laurent Desvillettes for helpful discussion and valuable comments. The author was supported by Engineering and Physical Sciences Research Council (EP/K00804/1) and ERC-Starting grant HDSPCONTR ?High-Dimensional Sparse Optimal Control?. This work is also supported by the Alexander Humboldt Foundation through the Humboldt Research Fellowship for Postdoctoral Researchers.

Funding Information:
The author also thanks Professor José A. Carrillo and Professor Laurent Desvillettes for helpful discussion and valuable comments. The author was supported by Engineering and Physical Sciences Research Council ( EP/K00804/1 ) and ERC -Starting grant HDSPCONTR “High-Dimensional Sparse Optimal Control”. This work is also supported by the Alexander Humboldt Foundation through the Humboldt Research Fellowship for Postdoctoral Researchers.

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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