Global well-posedness and exponential decay of strong solution for the three-dimensional inhomogeneous incompressible micropolar equations with density-dependent transport coefficients and large initial data

TL;DR

This paper proves the global existence and exponential decay of strong solutions for 3D inhomogeneous incompressible micropolar equations with density-dependent coefficients, allowing large initial data without size restrictions.

Contribution

It establishes the global well-posedness and decay properties for a complex fluid model with density-dependent viscosity, extending previous results to large initial data.

Findings

Global existence of strong solutions under large initial data

Exponential decay of solutions over time

No size restriction on initial velocity and micro-rotational velocity

Abstract

In this paper, we consider the Dirichlet problem of three-dimensional inhomogeneous incompressible micropolar equations with density-dependent viscosity. Under the assumption that the coefficients are power functions of the density, we establish the global existence of strong solutions as long as the initial density is linear equivalent to a large constant state. There is no restriction on the size of initial velocity and micro-rotational velocity. As a by-product, we prove the exponential decay for the solution.