### 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 |

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### 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