Dissipative solutions to a Beris-Edwards type model for compressible active nematic liquid crystals
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915708456140800 |
|---|---|
| author | Bhandari, Kuntal Majumdar, Apala Nečasová, Šárka |
| author_facet | Bhandari, Kuntal Majumdar, Apala Nečasová, Šárka |
| contents | We study the hydrodynamics of compressible active nematic liquid crystals in a three-dimensional and bounded domain, with a nonlinear viscosity tensor and nonhomogeneous boundary data, in a Landau-de Gennes framework. We prove the existence of dissipative solutions within a Beris-Edwards type model for active nematodynamics, which are weak solutions satisfying the underlying equations modulo a defect measure. The proof follows from a three level approximation scheme -- the Galerkin approximation, the classical parabolic regularization of the continuity equation, and the convex regularization of the potential generating the viscous stress. New techniques are required to deal with non-Newtonian stress tensor, larger classes of admissible pressure potentials and nonhomogeneous boundary conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02051 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dissipative solutions to a Beris-Edwards type model for compressible active nematic liquid crystals Bhandari, Kuntal Majumdar, Apala Nečasová, Šárka Analysis of PDEs We study the hydrodynamics of compressible active nematic liquid crystals in a three-dimensional and bounded domain, with a nonlinear viscosity tensor and nonhomogeneous boundary data, in a Landau-de Gennes framework. We prove the existence of dissipative solutions within a Beris-Edwards type model for active nematodynamics, which are weak solutions satisfying the underlying equations modulo a defect measure. The proof follows from a three level approximation scheme -- the Galerkin approximation, the classical parabolic regularization of the continuity equation, and the convex regularization of the potential generating the viscous stress. New techniques are required to deal with non-Newtonian stress tensor, larger classes of admissible pressure potentials and nonhomogeneous boundary conditions. |
| title | Dissipative solutions to a Beris-Edwards type model for compressible active nematic liquid crystals |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.02051 |