Abstract
We consider forced active scalar equations with even and homogeneous degree 0 drift operator on Td. Inspired by the non-uniqueness construction for dyadic fluid models (Dai and Friedlander, 2022; Filonov and Khodunov, 2021), by implementing a sum-difference convex integration scheme we obtain non-unique weak solutions for the active scalar equation in space Ct0Cxα with α<12d+1. Without external forcing, Isett and Vicol (2015) constructed non-unique weak solutions for such active scalar equations with spatial regularity Cxα for α<14d+1.
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