Remarks on Oldroyd-B and related complex fluid models

Peter Constantin, Weiran Sun

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

We prove global existence and uniqueness of solutions of Oldroyd-B systems, with relatively small data in ℝd, in a large functional setting (Cα ∩ L1). This is a stability result; solutions select an equilibrium and converge exponentially to it. Large spatial derivatives of the initial density and stress are allowed, provided the L norm of the density and stress are small enough. We prove global regularity for large data for a model in which the potential responds to high rates of strain in the fluid. We also prove global existence for a class of large data for a didactic scalar model which attempts to capture, in the simplest way, the essence of the dissipative nature of the coupling to fluid. This latter model has an unexpected cone invariance in function space that is crucial for the global existence.

Original languageEnglish (US)
Pages (from-to)33-73
Number of pages41
JournalCommunications in Mathematical Sciences
Volume10
Issue number1
DOIs
StatePublished - Mar 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Blow up
  • Complex fluids
  • Euler equations
  • Fokker-Planck equations
  • Global existence
  • Kinetic equations
  • Navier-Stokes equations
  • Oldroyd-B

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