### Abstract

Consider the (simplified) Leslie.Ericksen model for the flow of nematic liquid crystals in a bounded domain ω ⊂ ℝ^{n} for n <1. This article develops a complete dynamic theory for these equations, analyzing the system as a quasilinear parabolic evolution equation in an L_{p}-L_{q}-setting. First, the existence of a unique local strong solution is proved. 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 this case the solution converges exponentially to an equilibrium. Moreover, the solution is shown to be real analytic, jointly in time and space.

Original language | English |
---|---|

Pages (from-to) | 397-408 |

Number of pages | 12 |

Journal | Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis |

Volume | 33 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2016 Mar 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Convergence to equilibria
- Global solutions
- Nematic liquid crystals
- Quasilinear parabolic evolution equations
- Regularity

### ASJC Scopus subject areas

- Analysis
- Mathematical Physics

### Cite this

*Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis*,

*33*(2), 397-408. https://doi.org/10.1016/j.anihpc.2014.11.001

**Dynamics of nematic liquid crystal flows : The quasilinear approach.** / Hieber, Matthias Georg; Nesensohn, Manuel; Pruss, Jan; Schade, Katharina.

Research output: Contribution to journal › Article

*Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis*, vol. 33, no. 2, pp. 397-408. https://doi.org/10.1016/j.anihpc.2014.11.001

}

TY - JOUR

T1 - Dynamics of nematic liquid crystal flows

T2 - The quasilinear approach

AU - Hieber, Matthias Georg

AU - Nesensohn, Manuel

AU - Pruss, Jan

AU - Schade, Katharina

PY - 2016/3/1

Y1 - 2016/3/1

N2 - Consider the (simplified) Leslie.Ericksen model for the flow of nematic liquid crystals in a bounded domain ω ⊂ ℝn for n <1. This article develops a complete dynamic theory for these equations, analyzing the system as a quasilinear parabolic evolution equation in an Lp-Lq-setting. First, the existence of a unique local strong solution is proved. 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 this case the solution converges exponentially to an equilibrium. Moreover, the solution is shown to be real analytic, jointly in time and space.

AB - Consider the (simplified) Leslie.Ericksen model for the flow of nematic liquid crystals in a bounded domain ω ⊂ ℝn for n <1. This article develops a complete dynamic theory for these equations, analyzing the system as a quasilinear parabolic evolution equation in an Lp-Lq-setting. First, the existence of a unique local strong solution is proved. 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 this case the solution converges exponentially to an equilibrium. Moreover, the solution is shown to be real analytic, jointly in time and space.

KW - Convergence to equilibria

KW - Global solutions

KW - Nematic liquid crystals

KW - Quasilinear parabolic evolution equations

KW - Regularity

UR - http://www.scopus.com/inward/record.url?scp=84959516151&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959516151&partnerID=8YFLogxK

U2 - 10.1016/j.anihpc.2014.11.001

DO - 10.1016/j.anihpc.2014.11.001

M3 - Article

VL - 33

SP - 397

EP - 408

JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

SN - 0294-1449

IS - 2

ER -