On problems of regularity and existence for critical drift elliptic equations and systems

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.