Elliptic equations with a singular drift from a weak Morrey space

Abstract

In this paper we prove the existence and uniqueness of weak solutions to the Dirichlet problem for an elliptic equation with a drift $b$ satisfying $\mathrm{div}b\le 0$ in $\Omega$. We assume $b$ belongs to some weak Morrey class which includes in the 3D case, in particular, drifts having a singularity along the axis $x_3$ with the asymptotic $b(x)\sim c/r$, where $r=\sqrt{x_1^2+x_2^2}$.

References in corpus (5)

• Global well-posedness for an advection-diffusion equation arising in magneto-geostrophic dynamics
• A partial uniqueness result and an asymptotically sharp nonuniqueness result for the Zhikov problem on the torus
• On parabolic equations in Morrey spaces with VMO $a$ and Morrey $b,c$
• Linear and fully nonlinear elliptic equations with $L_d$-drift
• On the contraction properties for weak solutions to linear elliptic equations with $L^2$-drifts of negative divergence