PreprintarXiv licencearXiv
Numerical approximation of probabilistically strong solutions to the stochastic harmonic map heat flow
Abstract
We study the stochastic harmonic map heat flow into the sphere driven by a Stratonovich noise term that formally preserves the spherical constraint by construction. Starting from a fully discrete, implementable numerical scheme, we prove its convergence to the novel solution concept of probabilistically strong, analytically energy-variational solutions. This yields the first existence result for probabilistically strong solutions in the three-dimensional setting on the prescribed stochastic basis. In addition, we establish weak-strong uniqueness and illustrate our theoretical findings with numerical experiments.
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BibTeX
@misc{lasarzik2026numerical,
title = {{Numerical approximation of probabilistically strong solutions to the stochastic harmonic map heat flow}},
author = {Robert Lasarzik and Stefan Metzger and Maximilian E. V. Reiter},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32588},
eprint = {2610.32588},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32588},
}
RIS
TY - UNPB
TI - Numerical approximation of probabilistically strong solutions to the stochastic harmonic map heat flow
AU - Robert Lasarzik
AU - Stefan Metzger
AU - Maximilian E. V. Reiter
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32588
UR - https://arxiv.org/abs/2610.32588
AB - We study the stochastic harmonic map heat flow into the sphere driven by a Stratonovich noise term that formally preserves the spherical constraint by construction. Starting from a fully discrete, implementable numerical scheme, we prove its convergence to the novel solution concept of probabilistically strong, analytically energy-variational solutions. This yields the first existence result for probabilistically strong solutions in the three-dimensional setting on the prescribed stochastic basis. In addition, we establish weak-strong uniqueness and illustrate our theoretical findings with numerical experiments.
ER -