scholarly journals Global well-posedness and twist-wave solutions for the inertial Qian–Sheng model of liquid crystals

2018 ◽  
Vol 264 (2) ◽  
pp. 1080-1118 ◽  
Author(s):  
Francesco De Anna ◽  
Arghir Zarnescu
Keyword(s):  
Liquid Crystals ◽  
Well Posedness ◽  
Wave Solutions

scholarly journals Nematic Dispersive Shock Waves from Nonlocal to Local

2021 ◽  
Vol 11 (11) ◽  
pp. 4736
Author(s):  
Saleh Baqer ◽  
Dimitrios J. Frantzeskakis ◽  
Theodoros P. Horikis ◽  
Côme Houdeville ◽  
Timothy R. Marchant ◽  
...  
Keyword(s):  
Shock Wave ◽  
Liquid Crystals ◽  
Shock Waves ◽  
Numerical Solutions ◽  
Wave Structure ◽  
Beam Power ◽  
Input Beam ◽  
Shock Wave Structure ◽  
Wave Solutions ◽  
Modulation Theory

The structure of optical dispersive shock waves in nematic liquid crystals is investigated as the power of the optical beam is varied, with six regimes identified, which complements previous work pertinent to low power beams only. It is found that the dispersive shock wave structure depends critically on the input beam power. In addition, it is known that nematic dispersive shock waves are resonant and the structure of this resonance is also critically dependent on the beam power. Whitham modulation theory is used to find solutions for the six regimes with the existence intervals for each identified. These dispersive shock wave solutions are compared with full numerical solutions of the nematic equations, and excellent agreement is found.

On the Benney equation

2009 ◽  
Vol 139 (6) ◽  
pp. 1121-1144 ◽  
Author(s):  
Amin Esfahani
Keyword(s):  
Sobolev Spaces ◽  
Initial Value Problem ◽  
A Priori ◽  
Travelling Wave ◽  
Well Posedness ◽  
Travelling Wave Solutions ◽  
Initial Value ◽  
Wave Solutions ◽  
Benney Equation ◽  
Well Posed

We study the Benney equation and show that the associated initial-value problem is locally well-posed in Sobolev spaces Hs(ℝ2) for s > −2. Furthermore, we use a priori estimates to establish the global well-posedness for s ≥ 0. We also prove that these results are in some sense sharp. In addition, we obtain some exact travelling-wave solutions of the equation.

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