Abstract In this paper we investigate the existence, uniqueness and stability of weak solutions of the initial boundary value problem with the Dirichlet boundary conditions for a parabolic equation with a drift b L₂ b ∈ L 2. We prove uniform in time L₁ L 1 -stability of solutions with respect to perturbations of the drift b in L₂ L 2 in the case if the drift satisfies the “non-spectral” condition div b 0 div b ≤ 0.
Glazkov et al. (Tue,) studied this question.