Attractors for the Navier-Stokes-Cahn-Hilliard System with Chemotaxis and Singular Potential in 2D
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910765215121408 |
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| author | He, Jingning |
| author_facet | He, Jingning |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_06258 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Attractors for the Navier-Stokes-Cahn-Hilliard System with Chemotaxis and Singular Potential in 2D He, Jingning Analysis of PDEs 35A01, 35A02, 35K35, 35Q92, 76D05 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. |
| title | Attractors for the Navier-Stokes-Cahn-Hilliard System with Chemotaxis and Singular Potential in 2D |
| topic | Analysis of PDEs 35A01, 35A02, 35K35, 35Q92, 76D05 |
| url | https://arxiv.org/abs/2301.06258 |