Remarks on the two-dimensional magnetohydrodynamics system forced by space-time white noise
Analysis of PDEs
2023-08-21 v1 Probability
Abstract
We study the two-dimensional magnetohydrodynamics system forced by space-time white noise. Due to a lack of an explicit invariant measure, the approach of Da Prato and Debussche (2002, J. Funct. Anal., \textbf{196}, pp. 180--210) on the Navier-Stokes equations does not seem to fit. We follow instead the approach of Hairer and Rosati (2023, arXiv:2301.11059 [math.PR]), take advantage of the structure of Maxwell's equation, such as anti-symmetry, to find an appropriate paracontrolled ansatz and many crucial cancellations, and prove the global-in-time existence and uniqueness of its solution.
Keywords
Cite
@article{arxiv.2308.09692,
title = {Remarks on the two-dimensional magnetohydrodynamics system forced by space-time white noise},
author = {Kazuo Yamazaki},
journal= {arXiv preprint arXiv:2308.09692},
year = {2023}
}