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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:496

Article

Goudenege, Ludovic¹  Manca, Luigi² 

[1] Univ Paris Saclay, Federat Math Cent Supelec FR 3487, Cent Supelec, CNRS, F-91190 Gif Sur Yvette, France

[2] Univ Paris Est Creteil, Univ Gustave Eiffel, UPEM, LAMA,CNRS, F-77447 Marne La Vallee, France

关键词: Navier-Stokes;    Camassa-Holm;    Lagrange averaged alpha;    Stochastic partial differential equations;    Vescicle;    Interaction model;   

DOI  :  10.1016/j.jmaa.2020.124805

来源: Elsevier

【 摘 要 】

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 fluidwith 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 L-2 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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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