Nonlocal-to-local limit for linear transport equations with measure initial data

Immanuel Ben Porat

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arXiv · 2607.21968

Nonlocal-to-local limit for linear transport equations with measure initial data

Immanuel Ben Porat

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Abstract

We initiate the study of the nonlocal to local limit for linear transport equa- tions. A nonlocal version of the linear transport equation is introduced alongside an appropriate well-posedness theory for distributional solutions with measure initial data. We proceed by deriving the associated linear transport equation as a nonlocal-to-local limit. Some of the results apply in arbitrary dimension and for measure initial data.

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Immanuel Ben Porat. 2026-07-24. Nonlocal-to-local limit for linear transport equations with measure initial data. https://arxiv.org/abs/2607.21968

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