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arXiv · 2407.02364

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

Jules Pitcho
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Abstract

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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Jules Pitcho. 2024-07-02. On the stochastic selection of integral curves of a rough vector field. https://arxiv.org/abs/2407.02364

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