Generalized momenta of mass and their applications to the flow of compressible fluid

TL;DR

This paper introduces a technique based on generalized momenta of mass to analyze compressible fluid flow, leading to nonexistence results, solution constructions, and boundary behavior insights in fluid dynamics.

Contribution

It develops a novel method using generalized momenta of mass for analyzing compressible fluids, providing new theoretical results and solution constructions.

Findings

Nonexistence of certain solutions with rapid decay at infinity

Construction of solutions with uniform deformation

Analysis of material volume boundary behavior

Abstract

We present a technique that allows to obtain certain results in the compressible fluid theory: in particular, it is a nonexistence result for the highly decreasing at infinity solutions to the Navier-Stokes equations, the construction of the solutions with uniform deformation and the study of behavior of the boundary of a material volume of liquid.