Weighted estimates for the Oseen problem in \(\mathbb R^3\) (Q812745)

The authors consider the following Oseen approximation \[ -\Delta\vec u+{\partial\vec u\over\partial x_1}+ \nabla\pi= \vec f\quad\text{in }\mathbb R^3,\quad \text{div\,}\vec u= g,\quad\lim_{|x|\to\infty}\vec u(x)=\vec u_\infty, \] where a vector fields \(\vec f\) and \(\vec u_\infty\) and a function \(g\) are given. Using a framework of a weighted Sobolev spaces, the authors study asymptotics of some solutions.