Three-dimensional magnetohydrodynamics system forced by space-time white noise

dc.creatorYamazaki, Kazuo (TTU)
dc.date.accessioned2023-04-20T21:32:36Z
dc.date.available2023-04-20T21:32:36Z
dc.date.issued2023
dc.description© 2023, Institute of Mathematical Statistics. All rights reserved. cc-by
dc.description.abstractWe consider the three-dimensional magnetohydrodynamics system forced by noise that is white in both time and space. Its complexity due to four non-linear terms makes its analysis very intricate. Nevertheless, taking advantage of its structure and adapting the theory of paracontrolled distributions from [30], we prove its local well-posedness. A first challenge is to find an appropriate paracontrolled ansatz which must consist of both the velocity and the magnetic fields. Second challenge is that for some non-linear terms, renormalizations cannot be achieved individually; we overcome this obstacle by strategically coupling certain terms together rather than separately. Our proof is also inspired by the work of [70].
dc.identifier.citationYamazaki, K.. 2023. Three-dimensional magnetohydrodynamics system forced by space-time white noise. Electronic Journal of Probability, 28. https://doi.org/10.1214/23-EJP929
dc.identifier.urihttps://doi.org/10.1214/23-EJP929
dc.identifier.urihttps://hdl.handle.net/2346/93025
dc.language.isoeng
dc.subjectGaussian hypercontractivity
dc.subjectmagnetohydrodynamics system
dc.subjectparacontrolled distri-butions
dc.subjectrenormalization
dc.subjectWick products
dc.titleThree-dimensional magnetohydrodynamics system forced by space-time white noise
dc.typeArticle

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