Global well-posedness of the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system with Landau Potential
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914951785873408 |
|---|---|
| author | Rui, Nie Li, Fang Zhenhua, Guo |
| author_facet | Rui, Nie Li, Fang Zhenhua, Guo |
| contents | A diffuse-interface model that describes the dynamics of nonhomogeneous incompressible two-phase viscous flows is investigated in a bounded smooth domain in ${\mathbb R}^3.$ The dynamics of the state variables is described by the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system. We first give a blow-up criterion of local strong solution to the initial-boundary-value problem for the case of initial density away from zero. After establishing some key a priori with the help of the Landau Potential, we obtain the global existence and decay-in-time of strong solution, provided that the initial date $\|\nabla u_0\|_{L^{2}(Ω)}+\|\nabla μ_0\|_{L^{2}(Ω)}+ρ_0$ is suitably small. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11775 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system with Landau Potential Rui, Nie Li, Fang Zhenhua, Guo Analysis of PDEs A diffuse-interface model that describes the dynamics of nonhomogeneous incompressible two-phase viscous flows is investigated in a bounded smooth domain in ${\mathbb R}^3.$ The dynamics of the state variables is described by the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system. We first give a blow-up criterion of local strong solution to the initial-boundary-value problem for the case of initial density away from zero. After establishing some key a priori with the help of the Landau Potential, we obtain the global existence and decay-in-time of strong solution, provided that the initial date $\|\nabla u_0\|_{L^{2}(Ω)}+\|\nabla μ_0\|_{L^{2}(Ω)}+ρ_0$ is suitably small. |
| title | Global well-posedness of the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system with Landau Potential |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.11775 |