Nematic-isotropic phase transition in Beris-Edwards system at critical temperature

We are concerned with the sharp interface limit for the Beris-Edwards system in a bounded domain Omega subset of R-3 in this paper. The system can be described as the incompressible Navier-Stokes equations coupled with an evolution equation for the Q-tensor. We prove that the solutions to the Beris-Edwards system converge to the corresponding solutions of a sharp interface model under well-prepared initial data, as the thickness of the diffuse interfacial zone tends to zero. Moreover, we give not only the spatial decay estimates of the velocity vector field in the H-1 sense but also the error estimates of the phase field. The analysis relies on the relative entropy method and elaborated energy estimates. Published under an exclusive license by AIP Publishing.https://doi.org/10.1063/5.0246005