Global Yudovich-type solutions to a reduced model for micropolar fluids with zero viscosity

TL;DR

This paper establishes the global existence and uniqueness of Yudovich-type solutions for a two-dimensional reduced micropolar fluid model, extending classical Euler results to a coupled heterogenous system.

Contribution

It proves the first global well-posedness result for a micropolar fluid model with low regularity, combining Euler-type dynamics with microrotation effects.

Findings

Proves global existence of weak solutions with bounded vorticity and microrotation.

Extends Yudovich framework to a coupled heterogenous fluid system.

Demonstrates well-posedness at low regularity for micropolar fluids.

Abstract

In this paper, we study the well-posedeness at low regularity of a two-dimensional system obtained as a reduced model for micropolar fluid dynamics. At the mathematical level, the system presents a coupling between an Euler-type equation for the two-dimensional velocity field of the fluid and an advection-diffusion equation for the scalar microrotation field. For this model, we prove global existence and uniqueness of Yudovich-type solutions, namely weak solutions for which the vorticity is only bounded (with some additional integrability property) and the microrotation field remains bounded and of finite energy. To the best of our knowledge, this is the first result which extends the genuine Yudovich framework to a system obtained by perturbing the incompressible Euler equations with some sort of heterogeneity.