PreprintCC BY 4.0arXiv
Well-Posedness and Regularity for a Modified Liquid Crystal Model with Transport Noise
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 Lp-Lq frameworks with Besov initial data, including regimes of low and negative regularity.
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BibTeX
@misc{sarto2026wellposedness,
title = {{Well-Posedness and Regularity for a Modified Liquid Crystal Model with Transport Noise}},
author = {Gianmarco Del Sarto and Antoine Moneyron and Esmée Theewis and Tarek Zöchling},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38641},
eprint = {2610.38641},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38641},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Well-Posedness and Regularity for a Modified Liquid Crystal Model with Transport Noise
AU - Gianmarco Del Sarto
AU - Antoine Moneyron
AU - Esmée Theewis
AU - Tarek Zöchling
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38641
UR - https://arxiv.org/abs/2610.38641
AB - 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.
ER -