English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this paper we study a gradient flow generated by the Landau-de Gennes freeenergy that describes nematic liquid crystal configurations in the space of$Q$-tensors. This free energy density functional is composed of three quadraticterms as the elastic energy density part, and a singular potential in the bulkpart that is considered as a natural enforcement of a physical constraint onthe eigenvalues of $Q$. The system is a non-diagonal parabolic system with asingular potential which trends to infinity logarithmically when theeigenvalues of $Q$ approaches the physical boundary. We give a rigorous proofthat for rather general initial data with possibly infinite free energy, thesystem has a unique strong solution after any positive time $t_0$. Furthermore,this unique strong solution detaches from the physical boundary after asufficiently large time $T_0$. We also give estimate of the Hausdorff measureof the set where the solution touches the physical boundary and thus prove apartial regularity result of the solution in the intermediate stage $(0,T_0)$.

Regularity of a gradient flow generated by the anisotropic Landau-de Gennes energy with a singular potential