Long-Time Behavior of Global Weak Solutions for a Beris-Edwards Type Model of Nematic Liquid Crystals

Author:

Climent-Ezquerra BlancaORCID,Guillén-González Francisco

Abstract

AbstractWe consider a Beris-Edwards system modeling incompressible liquid crystal flows of nematic type. This system couples a Navier–Stokes system for the fluid velocity with a time-dependent system for the Q-tensor variable, whose spectral decomposition is related to the directors of liquid crystal molecules. The long-time behavior for global weak solutions is studied, proving that each whole trajectory converges to a single equilibrium whenever a regularity hypothesis is satisfied by the energy of the weak solution.

Funder

ministerio de ciencia, innovación y universidades

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Mathematics,Condensed Matter Physics,Mathematical Physics

Reference19 articles.

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3. Cavaterra, C., Rocca, E.: On a 3D isothermal model for nematic liquid crystals accounting for stretching terms. Z. Angew. Math. Phys. 64, 69–83 (2013)

4. Chen, G.Q., Majumdar, A., Wang, D., Zhang, R.: Global existence and regularity of solutions for active liquid crystals. J. Differ. Equ. 263, 202–239 (2017)

5. Chen, G.Q., Majumdar, A., Wang, D., Zhang, R.: Global weak solutions for the compressible active liquid crystal system Siam. J. Math. Anal. 50(4), 3632–3675 (2018)

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