Numerical approximation of probabilistically strong solutions to the stochastic harmonic map heat flow

Robert Lasarzik; Stefan Metzger; Maximilian E. V. Reiter

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arXiv · 2610.32588

Numerical approximation of probabilistically strong solutions to the stochastic harmonic map heat flow

Robert Lasarzik·Stefan Metzger·Maximilian E. V. Reiter

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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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Robert Lasarzik, Stefan Metzger, Maximilian E. V. Reiter. 2026-10-23. Numerical approximation of probabilistically strong solutions to the stochastic harmonic map heat flow. https://arxiv.org/abs/2610.32588

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