Well-posedness by noise for linear advection of \(k\)-forms

In this work, we extend existing well-posedness by noise results for the stochastic transport and continuity equations by treating them as special cases of the linear advection equation of \(k\)-forms, which arises naturally in geometric fluid dynamics. In particular, we prove the existence and uniq...

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Bibliographic Details
Published in:arXiv.org 2022-11
Main Authors: Aythami Bethencourt de Leon, So Takao
Format: Article
Language:English
Subjects:
Advection
Continuity equation
Fields (mathematics)
Noise
Well posed problems
Online Access:Get full text
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Summary:In this work, we extend existing well-posedness by noise results for the stochastic transport and continuity equations by treating them as special cases of the linear advection equation of \(k\)-forms, which arises naturally in geometric fluid dynamics. In particular, we prove the existence and uniqueness of weak \(L^p\)-solutions to the stochastic linear advection equation of \(k\)-forms that is driven by a H\"older continuous, \(W^{1,1}_{loc}\) drift and smooth diffusion vector fields, such that the equation without noise admits infinitely many solutions.
ISSN:2331-8422