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On elliptic equations with a singular drift from Morrey spaces

  • Timofey Shilkin (V.A. Steklov Mathematical Institute, St.-Petersburg, and Saarland University)
E1 05 (Leibniz-Saal)

Abstract

We investigate weak solutions to the Dirichlet problem for an elliptic equation with a drift b whose divergence is sign-defined. We assume b belongs to some weak Morrey class which includes in the 3D case, in particular, drifts having a singularity along the axis with the asymptotic c/r, where r is the distance to the axis. The problem under consideration is motivated by some questions arising in the theory of axially symmetric solutions to the Navier-Stokes equations. We present results on existence, uniqueness and local properties of weak solutions to this problem as well as its relation to the Navier-Stokes theory. Based on a joint work with M. Chernobai.

Anne Dornfeld

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