Global strong solutions to a compressible fluid-particle interaction model with density-dependent friction force
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| Format: | Preprint |
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2025
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| _version_ | 1866910150508412928 |
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| author | Li, Fucai Ni, Jinkai Wu, Man |
| author_facet | Li, Fucai Ni, Jinkai Wu, Man |
| contents | We investigate the Cauchy problem for a fluid-particle interaction model in $\mathbb{R}^3$. This model consists of the compressible barotropic Navier-Stokes equations and the Vlasov-Fokker-Planck equation coupled together via the density-dependent friction force. Due to the strong coupling caused by the friction force, it is a challenging problem to construct the global existence and optimal decay rates of strong solutions. In this paper, by assuming that the $H^2$-norm of the initial data is sufficiently small, we establish the global well-posedness of strong solutions. Furthermore, if the $L^1$-norm of initial data is bounded, then we achieve the optimal decay rates of strong solutions and their gradients in $L^2$-norm. The proofs rely on developing refined energy estimates and exploiting the frequency decomposition method. In addition, for the periodic domain case, our global strong solutions decay exponentially. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_19886 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global strong solutions to a compressible fluid-particle interaction model with density-dependent friction force Li, Fucai Ni, Jinkai Wu, Man Analysis of PDEs 76N06, 35Q84, 76N10, 35B40 We investigate the Cauchy problem for a fluid-particle interaction model in $\mathbb{R}^3$. This model consists of the compressible barotropic Navier-Stokes equations and the Vlasov-Fokker-Planck equation coupled together via the density-dependent friction force. Due to the strong coupling caused by the friction force, it is a challenging problem to construct the global existence and optimal decay rates of strong solutions. In this paper, by assuming that the $H^2$-norm of the initial data is sufficiently small, we establish the global well-posedness of strong solutions. Furthermore, if the $L^1$-norm of initial data is bounded, then we achieve the optimal decay rates of strong solutions and their gradients in $L^2$-norm. The proofs rely on developing refined energy estimates and exploiting the frequency decomposition method. In addition, for the periodic domain case, our global strong solutions decay exponentially. |
| title | Global strong solutions to a compressible fluid-particle interaction model with density-dependent friction force |
| topic | Analysis of PDEs 76N06, 35Q84, 76N10, 35B40 |
| url | https://arxiv.org/abs/2502.19886 |