Unique strong and V-attractor of a three-dimensional globally modified two-phase flow model

作者：Medjo T. Tachim^*

来源：Annali di Matematica Pura ed Applicata, 2018, 197(3): 843-868.

DOI：10.1007/s10231-017-0706-8

• Allen-Cahn-Navier-Stokes
• Globally modified
• Strong solutions
• Global attractor

In this article, we study a globally modified Allen-Cahn-Navier-Stokes system in a three-dimensional domain. The model consists of the globally modified Navier-Stokes equations proposed in Caraballo et al. (Adv Nonlinear Stud 6(3):411-436, 2006) for the velocity, coupled with an Allen-Cahn model for the order (phase) parameter. We prove the existence and uniqueness of strong solutions. Using the flattening property, we also prove the existence of global V-attractors for the model. Using a limiting argument, we derive the existence of bounded entire weak solutions for the three-dimensional coupled Allen-Cahn-Navier-Stokes system with time-independent forcing.

• 出版日期2018-6