On the integral representation of the solution to the Stokes system
The paper is a synthetic and critical analysis of the linearized Navier- Stokes system: \(\Delta v-\nabla p=f\), div v\(=g\), \(v|_{\partial \Omega}=\phi\). The method used by the author is the Green's one, by means of which he expresses the pressure and the velocity field in terms of \(\Omega\), f, g, \(\phi\). Theorems of existence and uniqueness are also proved. What is very interesting in the paper is its critical aspect, which put in discussion the very ancient results obtained by famous specialists in the viscous flow problems. The author finds some results of F. K. G. Odqvist, H. Villat, O. A. Ladyzhenskaya and other ones as incorrect, incomplete or not well-grounded. His unexpected remarks are very useful for all interested in the domain.
scientific article; zbMATH DE number 3953389
scientific article