Lp-theory for strong solutions to fluid-rigid body interaction in Newtonian and generalized Newtonian fluids

Matthias Geissert, Karoline Götze, Matthias Georg Hieber

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Consider the system of equations describing the motion of a rigid body immersed in a viscous, incompressible fluid of Newtonian or generalized Newtonian type. The class of fluids considered includes in particular shearthinning or shear-thickening fluids of power-law type of exponent d ≥ 1. We develop a method to prove that this system admits a unique, local, strong solution in the Lp-setting. The approach presented in the case of generalized Newtonian fluids is based on the theory of quasi-linear evolution equations and requires that the exponent p satisfies the condition p > 5.

Original languageEnglish
Pages (from-to)1393-1439
Number of pages47
JournalTransactions of the American Mathematical Society
Volume365
Issue number3
DOIs
Publication statusPublished - 2013
Externally publishedYes

Keywords

  • Fluid-rigid body interaction
  • Generalized Newtonian fluids
  • Strong L-solutions

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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