A phase-field system arising from multiscale modeling of thrombus biomechanics in blood vessels: local well-posedness in dimension two

We consider a phase-field model which describes the interactions between the blood flow and the thrombus. The latter is supposed to be a viscoelastic material. The potential describing the cohesive energy of the mixture is assumed to be of Flory-Huggins type (i.e. logarithmic). This ensures the boundedness from below of the dissipation energy. In the two dimensional case, we prove the local (in time) existence and uniqueness of a strong solution, provided that the two viscosities of the pure fluid phases are close enough. We also show that the order parameter remains strictly separated from the pure phases if it is so at the initial time.