\(L^p\)-weighted theory for Navier-Stokes equations in exterior domains
In this very interesting and technical paper, the exterior Navier-Stokes problem is considered. The flow is studied in an unbounded domain; the no-slip condition is considered on a part of boundary. Very important is the imposed behaviour of the velocity at infinity. The point is to improve some previous result of Farwing and Galdi, where the external force field \(f\) was considered in a classical \(L^p\) Lebesgue space. In the present paper, the external forces are considered in some generalized \(W\)-Sobolev spaces. For different regularity levels of \(f\), the corresponding existence and smoothness of the associated weak solutions are studied. The exterior Oseen problem is also considered. The important mathematical tools used in this paper are the unit partition result (introduced in Proposition 8) and some energetic inequalities.
scientific article; zbMATH DE number 5610815