### 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 |
---|---|

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 |

### Fingerprint

### 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

**On strong dynamics of compressible nematic liquid crystals.** / Schade, Katharina; Shibata, Yoshihiro.

Research output: Contribution to journal › Article

*SIAM Journal on Mathematical Analysis*, vol. 47, no. 5, pp. 3963-3992. https://doi.org/10.1137/140970628

}

TY - JOUR

T1 - On strong dynamics of compressible nematic liquid crystals

AU - Schade, Katharina

AU - Shibata, Yoshihiro

PY - 2015

Y1 - 2015

N2 - Given a uniform W3-1/q q -domain ω ⊆ ℝN 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.

AB - Given a uniform W3-1/q q -domain ω ⊆ ℝN 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.

KW - Compressible viscous fluid

KW - Global solutions

KW - Nematic liquid crystals

KW - Quasi-linear parabolic evolution equations

KW - Regularity

UR - http://www.scopus.com/inward/record.url?scp=84947466217&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84947466217&partnerID=8YFLogxK

U2 - 10.1137/140970628

DO - 10.1137/140970628

M3 - Article

VL - 47

SP - 3963

EP - 3992

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 5

ER -