Forward Self-Similar Solutions of the Navier-Stokes Equations in the Half Space

For the incompressible Navier-Stokes equations in the 3D half space, we show the existence of forward self-similar solutions for arbitrarily large self-similar initial data.Comment: Final version before publication. To appear in Analysis and PD

On Properties of the Intrinsic Geometry of Submanifolds in a Riemannian Manifold

In the paper we study the properties of a metric function which is the extension by continuity of the intrinsic metric of the interior of a submanifold to its boundary. This approach is the development of the classical intrinsic geometry of surfaces studied by A.D. Alexandrov and his school