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On a 1D transport equation with nonlocal velocity and supercritical dissipation

We study a 1D transport equation with nonlocal velocity. First, we prove eventual regularization of the viscous regularization when dissipation is in the supercritical range with non-negative initial data. Next, we will prove global regularity for solutions when dissipation is slightly supercritical. Both results utilize a nonlocal maximum principle.

preprint2013arXivOpen access
Tam Do
math.AP
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