Existence theory for generalized Newtonian fluids

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The flow of a homogeneous generalized Newtonian fluid is described by a generalized Navier-Stokes system whit a shear rate dependent viscocity. In the common power law model the stress deviator is given by S(epsilon(v)) = (1 + vertical bar epsilon(v)vertical bar)(p-2)epsilon(v) with p is an element of (1, infinity). In this note we give an overview about results concerning the existence of weak solutions to these equations in the stationary and non-stationary setting. We present the different techniques which are based on monotone operator theory, L-infinity-truncation and Lipschitz truncation respectively.

Original languageEnglish
Title of host publicationRecent Advances in Partial Differential Equations and Applications
EditorsV. D. Radulescu, A. Sequeira, V. A. Solonnikov
PublisherAmerican Mathematical Society
Pages99-110
Number of pages12
ISBN (Electronic)9781470434717
ISBN (Print)9781470415211
DOIs
Publication statusPublished - 2016
EventInternational Conference in honor of Hugo Beirao de Veiga's 70th Birthday: Recent Advances in PDEs and Applications - Levico Terme, Italy
Duration: 17 Feb 201421 Feb 2014

Publication series

NameContemporary Mathematics
PublisherAmerican Mathematical Society
Volume666
ISSN (Print)0271-4132

Conference

ConferenceInternational Conference in honor of Hugo Beirao de Veiga's 70th Birthday
CountryItaly
CityLevico Terme
Period17/02/1421/02/14

Keywords

  • Weak solutions
  • generalized Navier-Stokes equations
  • power law fluids
  • SHEAR-DEPENDENT VISCOSITY
  • SOLENOIDAL LIPSCHITZ TRUNCATION
  • POWER-LAW FLUIDS
  • WEAK SOLUTIONS
  • STEADY FLOWS

Cite this

Breit, D. (2016). Existence theory for generalized Newtonian fluids. In V. D. Radulescu, A. Sequeira, & V. A. Solonnikov (Eds.), Recent Advances in Partial Differential Equations and Applications (pp. 99-110). (Contemporary Mathematics; Vol. 666). American Mathematical Society. https://doi.org/10.1090/conm/666/13242