Attractors for the Navier-Stokes-Cahn-Hilliard System with Chemotaxis and Singular Potential in 2D

2023/01/16 by Jingning He, He, Jingning
Computer Science · Materials Science · Mathematics · #35A01 #35A02 #35K35 #35Q92 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Dynamics and Pattern Formation #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2301.06258

openalex publication_date 2023/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze the long-time behavior of solutions to a Navier-Stokes-Cahn-Hilliard system with chemotaxis effects and a solution-dependent mass source term. The fluid velocity satisfies the Navier-Stokes system, the phase field variable satisfies a convective Cahn-Hilliard equation with a singular potential (e.g., the Flory-Huggins type), the nutrient density satisfies an advection-diffusion-reaction. For the initial boundary value problem in 2D, we prove the existence of the global attractor in a suitable phase space. Furthermore, we obtain the existence of an exponential attractor, and it can be implied that the global attractor is of finite fractal dimension.

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