Strong solutions to the equations of flow and heat transfer in magnetic fluids with internal rotations (Q379496)

The purpose of the present work is the mathematical analysis of an initial boundary-value problem for the system of equations describing the flow and heat transfer in a magnetic fluid with internal rotations, when the fluid is subjected to the action of an external magnetic field. Consider the flow of an incompressible and viscous, Newtonian ferrofluid, filling a bounded domain \(D\) under the action of an external magnetic field. This magnetic field induces a demagnetizing field \(H\) and a magnetic induction B satisfying the constitutive law. The authors study the Cauchy problem in the \(H^2\)-framework, they obtain a local-in-time existence result of a strong solution, establish a blow-up criterium and a global-in-time existence result under smallness assumptions on the data. Collinearity is a good approximation when the internal rotation of colloidal particles can be neglected.