We study the existence of regular solutions incompressible stationary Navier–Stokes equations in n-dimensional Euclidean space with a given bounded external force compact support. In dimensions $$n\le 5$$ , such was known. this paper, we extend it to 15$$ .

A connection between the separability and the countable chain condition of spaces with L-property (a topological space X has L-property if for every topological space Y , separately continuous function f : X ×Y →R and open set I ⊆R, the set f −1(I) is an Fσ-set) is studied. We show that every completely regular Baire space with the L-property and the countable chain condition is separable and c...

We study Lipschitz differentiability spaces, a class of metric measure spaces introduced by Cheeger in [8]. We show that if an Ahlfors regular Lipschitz differentiability space has charts of maximal dimension, then, at almost every point, all its tangents are uniformly rectifiable. In particular, at almost every point, such a space admits a tangent that is isometric to a finite-dimensional Bana...

In this paper, we study the separtion axioms $T_0,T_1,T_2$ and $T_{5/2}$ on topological and semitopological residuated lattices and we show that they are equivalent on topological residuated lattices. Then we prove that for every infinite cardinal number $alpha$, there exists at least one nontrivial Hausdorff topological residuated lattice of cardinality $alpha$. In the follows, we obtain some ...

The purpose of the present paper is two-fold. The first is to describe the space of continuous functionals for the Smirnov space Ep(U), p ≥ 1, when U is a simply connected, bounded domain with Ahlfors regular boundary in terms of functions which are analytic in the complement U (or dual complement) and have a prescribed boundary behavior on ∂U . As an application of the above results, we give a...

In this paper, we prove that the \(C^0\) and \(C^1\) topologies are same on set of regular curves in 2-sphere whose tangent vectors Lipschitz continuous, a.e. existing geodesic curvatures essentially bounded an open interval. Besides, study subset consisting start end at given points with directions, is a Banach manifold.