Abstract
We study the free boundary of the porous medium equation with nonlocal drifts in dimension one. Under the assumption that the initial data has super-quadratic growth at the free boundary, we show that the solution is smooth in space and \(C^{2,1}_{{loc }}\) in time, and then the free boundary is \(C^{2,1}_{{loc }}\). Moreover if the drift is local, both the solution and the free boundary are smooth.
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