TY - Generic T1 - On the singular local limit for conservation laws with nonlocal fluxes Y1 - 2017 A1 - M. Colombo A1 - G. Crippa A1 - L.V. Spinolo KW - Local limit KW - Nonlocal conservation law KW - Nonlocal continuity equation KW - Singular limit AB - We give an answer to a question posed in [2], which can be loosely speaking formulated as follows. Consider a family of continuity equations where the velocity field is given by the convolution of the solution with a regular kernel. In the singular limit where the convolution kernel is replaced by a Dirac delta, one formally recovers a conservation law: can we rigorously justify this formal limit? We exhibit counterexamples showing that, despite numerical evidence suggesting a positive answer, one in general does not have convergence of the solutions. We also show that the answer is positive if we consider viscous perturbations of the nonlocal equations. In this case, in the singular local limit the solutions converge to the solution of the viscous conservation law. JF - IMATI Report Series PB - CNR-IMATI CY - Pavia UR - http://irs.imati.cnr.it/reports/irs17-14 ER -