Abstract
In this paper, we consider the Beris–Edwards system for incompressible nematic liquid crystal flows. The system under investigation consists of the Navier–Stokes equations for the fluid velocity u coupled with an evolution equation for the order parameter Q-tensor. One important feature of the system is that its elastic free energy takes a general form and in particular, it contains a cubic term that possibly makes it unbounded from below. In the two dimensional periodic setting, we prove that if the initial L∞-norm of the Q-tensor is properly small, then the system admits a unique global weak solution. The proof is based on the construction of a specific approximating system that preserves the L∞-norm of the Q-tensor along the time evolution.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
