Well-posedness by noise for linear advection of k-forms

2019/04/30 by Aythami Bethencourt de Léon, de Leon, Aythami Bethencourt, So Takao +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1904.13319

openalex publication_date 2019/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 L^p-solutions to the stochastic linear advection equation of k-forms that is driven by a Hölder continuous, W^1,1_loc drift and smooth diffusion vector fields, such that the equation without noise admits infinitely many solutions.

Citations

• Solution Properties of a 3D Stochastic Euler Fluid Equation
• Hölder, Sobolev, weak-type and BMO estimates in mixed-norm with weights for parabolic equations

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