### 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 language | English |
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Title of host publication | Recent Advances in Partial Differential Equations and Applications |

Editors | V. D. Radulescu, A. Sequeira, V. A. Solonnikov |

Publisher | American Mathematical Society |

Pages | 99-110 |

Number of pages | 12 |

ISBN (Electronic) | 9781470434717 |

ISBN (Print) | 9781470415211 |

DOIs | |

Publication status | Published - 2016 |

Event | International Conference in honor of Hugo Beirao de Veiga's 70th Birthday: Recent Advances in PDEs and Applications - Levico Terme, Italy Duration: 17 Feb 2014 → 21 Feb 2014 |

### Publication series

Name | Contemporary Mathematics |
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Publisher | American Mathematical Society |

Volume | 666 |

ISSN (Print) | 0271-4132 |

### Conference

Conference | International Conference in honor of Hugo Beirao de Veiga's 70th Birthday |
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Country | Italy |

City | Levico Terme |

Period | 17/02/14 → 21/02/14 |

### 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