Strong Solutions, Global Regularity, and Stability of a Hydrodynamic System Modeling Vesicle and Fluid Interactions
Strong Solutions, Global Regularity, and Stability of a Hydrodynamic System Modeling Vesicle and Fluid Interactions
In this paper, we study a hydrodynamic system modeling the deformation of vesicle membranes in incompressible viscous fluids. The system consists of the Navier--Stokes equations coupled with a fourth-order phase-field equation. In the three-dimensional case, we prove the existence/uniqueness of local strong solutions for arbitrary initial data as well as …