A Phase Field Alpha-navier-stokes Vesicle-fluid Interaction Model: Existence And Uniqueness Of Solutions

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)In this work we analyze a system of nonlinear evolution partial differential equations modeling the fluid-structure interaction associated to the dynamics of an elastic vesicle immersed in a moving incompressible viscous fluid. This system of equations couples an equation for a phase field variable, used to determine the position of vesicle membrane deformed by the action of the fluid, to the alpha-Navier- Stokes equations with an extra nonlinear interaction term. We prove global in time existence and uniqueness of solutions for this system in suitable functional spaces even in the three-dimensional case.202397422Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CNPq [305467/2011-5]FAPESP [2009/15098-0