### Abstract

The general Ericksen-Leslie model for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal simplified model is then investigated analytically. A fairly complete dynamic theory is developed by analyzing these systems as quasilinear parabolic evolution equations in an L_{p} − L_{q}-setting. First, the existence of a unique, local strong solution is proved. It is then shown that this solution extends to a global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the natural norm of the underlying state space. In these cases the solution converges exponentially to an equilibrium in the natural state manifold.

Original language | English |
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Title of host publication | Mathematical Fluid Dynamics, Present and Future |

Publisher | Springer New York LLC |

Pages | 433-459 |

Number of pages | 27 |

Volume | 183 |

ISBN (Print) | 9784431564553 |

DOIs | |

Publication status | Published - 2016 |

Externally published | Yes |

Event | 8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014 - Tokyo, Japan Duration: 2014 Nov 11 → 2014 Nov 14 |

### Other

Other | 8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014 |
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Country | Japan |

City | Tokyo |

Period | 14/11/11 → 14/11/14 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematical Fluid Dynamics, Present and Future*(Vol. 183, pp. 433-459). Springer New York LLC. https://doi.org/10.1007/978-4-431-56457-7_15

**Thermodynamical consistent modeling and analysis of nematic liquid crystal flows.** / Hieber, Matthias Georg; Prüss, Jan.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Mathematical Fluid Dynamics, Present and Future.*vol. 183, Springer New York LLC, pp. 433-459, 8th CREST-SBM nternational Conference on Mathematical Fluid Dynamics, Present and Future, 2014, Tokyo, Japan, 14/11/11. https://doi.org/10.1007/978-4-431-56457-7_15

}

TY - GEN

T1 - Thermodynamical consistent modeling and analysis of nematic liquid crystal flows

AU - Hieber, Matthias Georg

AU - Prüss, Jan

PY - 2016

Y1 - 2016

N2 - The general Ericksen-Leslie model for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal simplified model is then investigated analytically. A fairly complete dynamic theory is developed by analyzing these systems as quasilinear parabolic evolution equations in an Lp − Lq-setting. First, the existence of a unique, local strong solution is proved. It is then shown that this solution extends to a global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the natural norm of the underlying state space. In these cases the solution converges exponentially to an equilibrium in the natural state manifold.

AB - The general Ericksen-Leslie model for the flow of nematic liquid crystals is reconsidered in the non-isothermal case aiming for thermodynamically consistent models. The non-isothermal simplified model is then investigated analytically. A fairly complete dynamic theory is developed by analyzing these systems as quasilinear parabolic evolution equations in an Lp − Lq-setting. First, the existence of a unique, local strong solution is proved. It is then shown that this solution extends to a global strong solution provided the initial data are close to an equilibrium or the solution is eventually bounded in the natural norm of the underlying state space. In these cases the solution converges exponentially to an equilibrium in the natural state manifold.

UR - http://www.scopus.com/inward/record.url?scp=85009802338&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85009802338&partnerID=8YFLogxK

U2 - 10.1007/978-4-431-56457-7_15

DO - 10.1007/978-4-431-56457-7_15

M3 - Conference contribution

AN - SCOPUS:85009802338

SN - 9784431564553

VL - 183

SP - 433

EP - 459

BT - Mathematical Fluid Dynamics, Present and Future

PB - Springer New York LLC

ER -