UBC DG MP PDE Seminar: Misha Chernobai

We investigate the weak solvability and properties of weak solutions to the Dirichlet problem for a scalar elliptic equation Δu+b(α)⋅∇u=f in a bounded domain Ω⊂ℝ2containing the origin, where f∈W−1q(Ω) with q>2 and b(α):=b−αx|x|2 , b is a divergence-free vector field and α∈ℝ is a parameter. Then we further improved this result to three dimensional case with a bounded domain Ω⊂ℝ3 and drift b(α):=b−αx′|x′|2, where x′=(x1,x2,0).