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Well-posedness by noise for linear advection of $k$-forms (1904.13319v3)
Published 30 Apr 2019 in math.AP, math-ph, math.DG, math.MP, and math.PR
Abstract: 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 $Lp$-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.