We prove the existence, uniqueness and regularity of weak solutions to the Dirichlet problem for an elliptic equation with a drift b and related result for L^q gradient estimates for perturbed Stokes system. We assume b belongs to weak Morrey class which includes in the 3D case, in particular, drifts having a singularity along the axis x_3. For perturbed Stokes system we consider drift from critical L^n space.
Misha Chernobai completed their PhD at UBC and specialist degree at Saint-Petersburg state university. Their main field of study are non-linear PDE's related to fluid dynamics.