On the stationary solutions of the 2D Doi-Onsager model

DOI10.1016/j.na.2010.06.012zbMath1217.34032OpenAlexW2007822819MaRDI QIDQ988133

Congming Li, Guofang Wang, Wenxiong Chen

Publication date: 26 August 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.06.012

zbMATH Keywords

existence of solutionsvariational methodsmultiplicity of solutionsaxial symmetry2D Doi-Onsager model

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Variational principles in infinite-dimensional spaces (58E30) Applications of boundary value problems involving ordinary differential equations (34B60) Linear boundary value problems for ordinary differential equations (34B05)

Related Items

Modelling and computation of liquid crystals, On the stationary solutions of Doi-Onsager model in general dimension, Critical points and bifurcations of the three-dimensional Onsager model for liquid crystals, Liouville type theorem to an integral system in the half-space, Nematic first order phase transition for liquid crystals in the van der Waals–Kac limit, Long-time behaviour and phase transitions for the McKean-Vlasov equation on the torus, On stationary solutions of the 2D Doi-Onsager model

Cites Work

• Multiple branches of ordered states of polymer ensembles with the Onsager excluded volume potential
• Global orientation dynamics for liquid crystalline polymers
• Asymptotic states of a Smoluchowski equation
• Remarks on a Smoluchowski equation
• Steady state solutions of the Smoluchowski equation for rigid nematic polymers under imposed fields
• Axial symmetry and classification of stationary solutions of Doi-Onsager equation on the sphere with Maier-Saupe potential
• A note on the Onsager model of nematic phase transitions
• The structure of equilibrium solutions of the one-dimensional Doi equation
• Note on the number of steady states for a two-dimensional Smoluchowski equation
• Critical points of the Onsager functional on a sphere
• A new proof on axisymmetric equilibria of a three-dimensional Smoluchowski equation