Weak-strong uniqueness of the full coupled Navier-Stokes and Q-tensor system in dimension three

2025/07/12 by Yang, Fan, Zhou, Junjie
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.09281

Abstract

In this paper, we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the Beris-Edwards model of nematic liquid crystals in ℝ³ with an arbitrary parameter ξ∈ℝ, which measures the ratio of tumbling and alignment effects caused by the flow. This result is obtained by proposing a new uniqueness criterion in terms of (ΔQ,∇ u) with regularity L_t^qL_x^p for (2)/(q)+(3)/(p)=(3)/(2) and 2≤ p≤ 6, which enable us to deal with the additional nonlinear difficulties arising from the parameter ξ. Comparing with the results of related literature, our finding also reveals a new regime of weak-strong uniqueness for the simplified case of ξ=0. Moreover, we establish the global well-posedness of this model for small initial data in H^s-framework.

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