On an initial-boundary value problem for the Stokes systems arising in the study of a problem with a free boundary
The author solves the initial-boundary value problem \[ v_ t-\nu \nabla^ 2v+\nabla p=f,\quad \nabla \cdot v=\rho (x,t),\quad v(x,0)=v_ 0(x), \] \[ T_ n-\sigma n(n\cdot \Delta_{\Gamma}\int^{t}_{0}vd\tau)|_{G_ T}=d(x,t)\text{ in } Q_ T=\Omega \times (0,T),\quad \Omega \subset {\mathbb{R}}^ 3, \] T\(=T(v,p)\) is a stress tensor and \(\Delta_{\Gamma}\) is the Laplace- Beltrami operator. The problem is solved in Sobolev-Slobodetskij spaces.
scientific article; zbMATH DE number 4208684