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arXiv · 1304.4296

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

Tam Do
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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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Tam Do. 2013-10-23. On a 1D transport equation with nonlocal velocity and supercritical dissipation. https://arxiv.org/abs/1304.4296

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