### Abstract

Given a uniform W^{3-1/q}
_{q} -domain ω ⊆ ℝ^{N} for N q ∞, we consider a simplified Ericksen.Leslie system modeling the flow of compressible nematic liquid crystals based on Lin and Liu [Comm. Pure Appl. Math., 48 (1995), pp. 501.537]. We show the unique existence of local-intime strong solutions. Furthermore, if ω is bounded and initial data are chosen suitably small, we obtain global-in-time strong solutions. Our approach is based on maximal regularity estimates of the compressible Navier.Stokes equation by Enomoto, von Below, and Shibata [Ann. Univ. Ferrara, 60 (2014), pp. 55.89] and maximal regularity estimates for the Neumann problem as a consequence of Weis-fs 2001 vector-valued Fourier multiplier theorem.

Original language | English |
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Pages (from-to) | 3963-3992 |

Number of pages | 30 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 47 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2015 |

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### Keywords

- Compressible viscous fluid
- Global solutions
- Nematic liquid crystals
- Quasi-linear parabolic evolution equations
- Regularity

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics
- Computational Mathematics

### Cite this

*SIAM Journal on Mathematical Analysis*,

*47*(5), 3963-3992. https://doi.org/10.1137/140970628