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

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.

22 pages