Tam Do
Published 2013-04-15, updated 2013-10-23Version 3
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.
Formation of singularities for a transport equation with nonlocal velocity
Time periodic solutions to the $2$D quasi-geostrophic equation with the supercritical dissipation
Periodic solutions for a 1D-model with nonlocal velocity via mass transport
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