Stochastic curve shortening flow driven by a transport-type pure jump L\'evy noise
Probability
2026-05-12 v1
Abstract
We study the existence and uniqueness, the regularity, and the long-time behavior of strong solutions to stochastic curve shortening flow driven by a transport-type pure jump L\'evy noise. To obtain the existence and uniqueness of strong solutions, we transform the equation into its equivalent It\^{o}-type stochastic partial differential equation via a transport equation, and apply the monotone method with Lyapunov-type conditions. The obstacles to investigate the long-time behavior are the weak dissipativity and singularity inherent in the equation. To this end, we establish an improved regularity and prove that these solutions converge pathwise to zero at an exponential rate.
Cite
@article{arxiv.2605.10609,
title = {Stochastic curve shortening flow driven by a transport-type pure jump L\'evy noise},
author = {Xiaotian Ge and Shijie Shang and Weina Wu and Jianliang Zhai},
journal= {arXiv preprint arXiv:2605.10609},
year = {2026}
}
Comments
17 pages