A priori estimates for the system modelling nonhomogeneous asymmetric fluids

TL;DR

This paper establishes preliminary bounds for a complex PDE system modeling the nonstationary flow of nonhomogeneous asymmetric fluids, involving velocity, angular velocity, density, and pressure in a bounded domain.

Contribution

It provides new a priori estimates for a PDE system describing nonhomogeneous asymmetric fluid flow, incorporating Helmholtz decomposition for density functions.

Findings

Derived bounds for velocity and angular velocity fields

Established estimates for density and pressure distributions

Applied Helmholtz decomposition to density functions

Abstract

In this paper, we prove some a priori estimates for a system of partial differential equations arising in the nonstationary flow of a nonhomogeneous incompressible asymmetric fluid in a bounded domain with smooth boundary. The unknowns of the system are the velocity field of the fluid particles, the angular velocity of rotation of the fluid particles, the mass density of the fluid and the pressure distribution. For the density functions we consider the application of the Helmholtz decomposition.