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Global well-posedness of the primitive equations with stochastic wind-driven boundary conditions
Abstract
Consider the three-dimensional primitive equations subject to Neumann wind stress driven by finitely many Brownian motions. For arbitrary smooth spatial wind profiles, global pathwise existence and uniqueness without assuming a vertical derivative of the initial datum is proved, extending the local theory of Binz, Hieber, Hussein, and Saal: The primitive equations with stochastic wind driven boundary conditions (J. Math. Pures Appl. (9) (2024), 76--101) for this class of data and wind profiles. The proof combines a local maximal rL2 regularity construction with weighted estimates for the boundary stochastic convolution.
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BibTeX
@misc{zoechling2026global,
title = {{Global well-posedness of the primitive equations with stochastic wind-driven boundary conditions}},
author = {Tarek Zoechling},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11734},
eprint = {2609.11734},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11734},
}
RIS
TY - UNPB
TI - Global well-posedness of the primitive equations with stochastic wind-driven boundary conditions
AU - Tarek Zoechling
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.11734
UR - https://arxiv.org/abs/2609.11734
AB - Consider the three-dimensional primitive equations subject to Neumann wind stress driven by finitely many Brownian motions. For arbitrary smooth spatial wind profiles, global pathwise existence and uniqueness without assuming a vertical derivative of the initial datum is proved, extending the local theory of Binz, Hieber, Hussein, and Saal: The primitive equations with stochastic wind driven boundary conditions (J. Math. Pures Appl. (9) (2024), 76--101) for this class of data and wind profiles. The proof combines a local maximal rL^2 regularity construction with weighted estimates for the boundary stochastic convolution.
ER -