Uniqueness and continuous dependence of solutions to the incompressible micropolar flows forward and backward in time

Abstract

This paper studies the continuous dependence of the solutions for the boundary-initial and boundary-final value problems associated with the incompressible micropolar flows. For the incompressible micropolar flows forward in time, the continuous dependence of solutions with respect to the changes in the body force and body couple and in the initial data is established by means of a method based on a Gronwall-type inequality, while an adapted version of the logarithmic convexity method is used to study the continuous dependence of solutions for the incompressible micropolar flows backward in time. As a direct consequence, some uniqueness results are obtained.