Solutions of the nonlocal linear transport equation ∂_t u^ε + B·∇(η_ε*u^ε)=0 converge to the local transport equation ∂_t u + B·∇u=0 as ε→0 for measure initial data and in arbitrary dimension.
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Nonlocal-to-local limit for linear transport equations with measure initial data
Solutions of the nonlocal linear transport equation ∂_t u^ε + B·∇(η_ε*u^ε)=0 converge to the local transport equation ∂_t u + B·∇u=0 as ε→0 for measure initial data and in arbitrary dimension.