Stochastic phase field α-Navier-Stokes vesicle-fluid interaction model

• Published in: Journal of mathematical analysis and applications Vol. 496; no. 1; p. 124805
• Main Authors: Goudenège, Ludovic, Manca, Luigi
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.04.2021; Elsevier
• Subjects: Analysis of PDEs; Camassa-Holm; Interaction model; Lagrange averaged alpha; Mathematics; Navier-Stokes; Probability; Stochastic partial differential equations; Vescicle; Interaction model; Navier-Stokes; Camassa-Holm; Stochastic partial differential equations; Vescicle; Lagrange averaged alpha; Lagrange Averaged alpha; stochastic partial differential equations; vesicle; fluid; interaction model; and phrases : Navier-Stokes
• ISSN: 0022-247X; 1096-0813
• DOI: 10.1016/j.jmaa.2020.124805

We consider a stochastic perturbation of the phase field alpha-Navier-Stokes model with vesicle-fluid interaction. It consists in 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 a phase-field equation -for the interface between the fluid and the vesicle- to the alpha-Navier-Stokes equation -for the viscous fluid- with an extra nonlinear interaction term, namely the bending energy. The stochastic perturbation is an additive space-time noise of trace class on each equation of the system. We prove the existence and uniqueness of solution in classical spaces of L2 functions with estimates of non-linear terms and bending energy. It is based on a priori estimate about the regularity of solutions of finite dimensional systems, and tightness of the approximated solution.