Quantitative unique continuation for a parabolic equation

We address the quantitative uniqueness properties of the solutions of the parabolic equation $ \partial_t u - \Delta u = w_j (x,t) \partial_j u

• v(x,t) u $where$v$and$w$arebounded\mathrm{.}Weprovethatforsolutions$u$, the order of vanishing is bounded by $C(\Vert v\Vert_{L^\infty}^{2/3}+\Vert w\Vert_{L^\infty}^2)$ matching the upper bound previously established in the elliptic case. in the elliptic case.