On the L₁–stability for parabolic equations with a supercritical drift term

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 .