On mappings with hydrodynamical normalization conditions in Euclidean space

TL;DR

This paper investigates classes of spatial mappings with hydrodynamical growth conditions in Euclidean space, establishing their equicontinuity under quasiconformal constraints and analyzing their convergence properties.

Contribution

It introduces and analyzes new classes of mappings with hydrodynamical normalization conditions, proving their equicontinuity and convergence behavior under quasiconformal and integral constraints.

Findings

Mappings form equicontinuous families under certain conditions.

Results on the closeness of classes with respect to locally uniform convergence.

Analysis of inverse mappings within these classes.

Abstract

We are studying spatial mappings that satisfy some space analog of a hydrodynamical type of growth in the neighborhood of the infinity. It is proved that homeomorphisms of the specified class form equicontinuous families under some conditions on their characteristic of quasiconformality. We have also considered the problem of closeness of these classes with respect to locally uniform convergence. We have obtained corresponding results for mappings with integral constraints, as well as for classes of corresponding inverse mappings.