On the local existence for an active scalar equation in critical regularity setting

Walter Rusin, Fei Wang

In this note, we address the local well-posedness for the active scalar equation ${\partial }_t\theta +u\cdot \nabla \theta =0$, where $u=-{\nabla }^{\perp }(-\Delta {)}^{-1+\beta /2}\theta$. The local existence of…