Abstract
In this paper we study a mathematical model for the dynamics of vesicle membranes in a 3D incompressible viscous fluid. The system is in the Eulerian formulation, involving the coupling of the incompressible Navier–Stokes system with a phase field equation. This equation models the vesicle deformations under external flow fields. We prove the local in time existence and uniqueness of strong solutions. Moreover, we show that, given T > 0, for initial data which are small (in terms of T), these solutions are defined on [0, T] (almost global existence).
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Communicated by G.P. Galdi
The work of the three authors was partially supported by ANR Grant BLAN07-2 202879 and by ANR Grant 09-BLAN-0213-02.
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Liu, Y., Takahashi, T. & Tucsnak, M. Strong Solutions for a Phase Field Navier–Stokes Vesicle–Fluid Interaction Model. J. Math. Fluid Mech. 14, 177–195 (2012). https://doi.org/10.1007/s00021-011-0059-9
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DOI: https://doi.org/10.1007/s00021-011-0059-9