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

Jingning He

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arXiv · 2301.06258

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

Jingning He

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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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Jingning He. 2023-01-16. Attractors for the Navier-Stokes-Cahn-Hilliard System with Chemotaxis and Singular Potential in 2D. https://arxiv.org/abs/2301.06258

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