On a 1D transport equation with nonlocal velocity and supercritical dissipation |
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Authors: | Tam Do |
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Institution: | Dept. of Mathematics, University of Wisconsin, Madison, USA |
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Abstract: | 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. |
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Keywords: | Active scalar Supercritical dissipation Nonlocal velocity Modulus of continuity |
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