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On the stochastic selection of integral curves of a rough vector field

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arxiv 2407.02364 v3 pith:3FBTY5WM submitted 2024-07-02 math.AP math.CAmath.PR

Jules Pitcho This is my paper · ORCID
classification math.APmath.CAmath.PR
keywords vectorcurvesfieldintegraldepauwincompressiblemeasureprove
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We prove that for bounded, divergence-free vector fields b in L^1_{loc}((0,1];BV(\T^d;\R^d)), there exists a unique incompressible measure on integral curves of b. We recall the vector field constructed by Depauw in [Depauw, C. R. Math. Acad. Sci. Paris, 2003], which lies in the above class, and prove that for this vector field, the unique incompressible measure on integral curves exhibits stochasticity.

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  1. On vanishing diffusivity selection for the advection equation

    math.AP 2024-11 accept novelty 6.0 of 10

    Vanishing diffusivity uniquely selects the solution of the advection equation for divergence-free BV vector fields singular only at the initial time, including Depauw's non-uniqueness example.

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