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arXiv · 2610.38641

Well-Posedness and Regularity for a Modified Liquid Crystal Model with Transport Noise

Gianmarco Del Sarto·Antoine Moneyron·Esmée Theewis·Tarek Zöchling
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Abstract

We prove well-posedness for a stochastic Lin-Liu model of modified liquid crystals, coupling an incompressible fluid to a director field under transport and multiplicative noise. On smooth bounded domains in two dimensions, we prove global well-posedness for energy-class initial data, provided the leading coefficient of the polynomial director potential is positive. On the torus, we establish local well-posedness in time-weighted $L^p$-$L^q$ frameworks with Besov initial data, including regimes of low and negative regularity.

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Gianmarco Del Sarto, Antoine Moneyron, Esmée Theewis, Tarek Zöchling. 2026-10-28. Well-Posedness and Regularity for a Modified Liquid Crystal Model with Transport Noise. https://arxiv.org/abs/2610.38641

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