Interior epsilon-regularity theory for the solutions of the magneto-micropolar equations with a perturbation term

Diego Chamorro (1) , David Llerena (1)

1 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry

We develop here a particular version of the partial regularity theory for the Magneto-Micropolar equations (MMP) where a perturbation term is added. These equations are used in some special cases, such as in the study of the evolution of liquid cristals or polymers, where the classical Navier-Stokes equations are not an accurate enough model. The incompressible Magneto-Micropolar system is composed of three coupled equations: the first one is based in the Navier-Stokes system, the second one considers mainly the magnetic field while the last equation introduces the microrotation field representing the angular velocity of the rotation of the fluid particles. External forces are considered and a specific perturbation term is added as it is quite useful in some applications.

Mots clés: Magneto-Micropolar equations; Partial Regularity Theory; Morrey spaces MSC2020: 35B65; 35Q35; 76D03

Domaines: Equations aux dérivées partielles [math.AP]

Diego Chamorro, David Llerena. Interior epsilon-regularity theory for the solutions of the magneto-micropolar equations with a perturbation term. Journal of Elliptic and Parabolic Equations, 2022, 8, pp.555-616. ⟨hal-03423564⟩