A Fractional Chemotaxis Navier–Stokes System with Matrix-Valued Sensitivities and Attractive–Repulsive Signals
In this paper, we considered a fractional chemotaxis fluid system with matrix-valued sensitivities and attractive–repulsive signals on a two-dimensional periodic torus <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics>&...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/3/209 |
| _version_ | 1797611679097290752 |
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| author | Chao Jiang Zuhan Liu Yuzhu Lei |
| author_facet | Chao Jiang Zuhan Liu Yuzhu Lei |
| author_sort | Chao Jiang |
| collection | DOAJ |
| description | In this paper, we considered a fractional chemotaxis fluid system with matrix-valued sensitivities and attractive–repulsive signals on a two-dimensional periodic torus <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">T</mi><mn>2</mn></msup></semantics></math></inline-formula>. This model describes the interaction between a type of cell that proliferates following a logistic law, and the diffusion of cells is fractional Laplace diffusion. The cells and attractive–repulsive signals are transported by a viscous incompressible fluid under the influence of a force due to the aggregation of cells. We proved the existence and uniqueness of the global classical solution on the matrix-valued sensitivities, and the initial data satisfied the regular conditions. Moreover, by using energy functionals, the stabilization of global bounded solutions of the system was proven. |
| first_indexed | 2024-03-11T06:31:11Z |
| format | Article |
| id | doaj.art-8cd94deeda09461caae0cd584b32f0ee |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T06:31:11Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-8cd94deeda09461caae0cd584b32f0ee2023-11-17T11:11:50ZengMDPI AGFractal and Fractional2504-31102023-02-017320910.3390/fractalfract7030209A Fractional Chemotaxis Navier–Stokes System with Matrix-Valued Sensitivities and Attractive–Repulsive SignalsChao Jiang0Zuhan Liu1Yuzhu Lei2School of Mathematical Science, Yangzhou University, Yangzhou 225002, ChinaSchool of Mathematical Science, Yangzhou University, Yangzhou 225002, ChinaSchool of Mathematical Science, Yangzhou University, Yangzhou 225002, ChinaIn this paper, we considered a fractional chemotaxis fluid system with matrix-valued sensitivities and attractive–repulsive signals on a two-dimensional periodic torus <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">T</mi><mn>2</mn></msup></semantics></math></inline-formula>. This model describes the interaction between a type of cell that proliferates following a logistic law, and the diffusion of cells is fractional Laplace diffusion. The cells and attractive–repulsive signals are transported by a viscous incompressible fluid under the influence of a force due to the aggregation of cells. We proved the existence and uniqueness of the global classical solution on the matrix-valued sensitivities, and the initial data satisfied the regular conditions. Moreover, by using energy functionals, the stabilization of global bounded solutions of the system was proven.https://www.mdpi.com/2504-3110/7/3/209chemotaxis Navier–Stokesmatrix-valued sensitivitiesfractional diffusionglobal classical solutionasymptotic stability |
| spellingShingle | Chao Jiang Zuhan Liu Yuzhu Lei A Fractional Chemotaxis Navier–Stokes System with Matrix-Valued Sensitivities and Attractive–Repulsive Signals Fractal and Fractional chemotaxis Navier–Stokes matrix-valued sensitivities fractional diffusion global classical solution asymptotic stability |
| title | A Fractional Chemotaxis Navier–Stokes System with Matrix-Valued Sensitivities and Attractive–Repulsive Signals |
| title_full | A Fractional Chemotaxis Navier–Stokes System with Matrix-Valued Sensitivities and Attractive–Repulsive Signals |
| title_fullStr | A Fractional Chemotaxis Navier–Stokes System with Matrix-Valued Sensitivities and Attractive–Repulsive Signals |
| title_full_unstemmed | A Fractional Chemotaxis Navier–Stokes System with Matrix-Valued Sensitivities and Attractive–Repulsive Signals |
| title_short | A Fractional Chemotaxis Navier–Stokes System with Matrix-Valued Sensitivities and Attractive–Repulsive Signals |
| title_sort | fractional chemotaxis navier stokes system with matrix valued sensitivities and attractive repulsive signals |
| topic | chemotaxis Navier–Stokes matrix-valued sensitivities fractional diffusion global classical solution asymptotic stability |
| url | https://www.mdpi.com/2504-3110/7/3/209 |
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