Global existence and uniqueness of the density-dependent incompressible Navier-Stokes-Korteweg system with variable capillarity and viscosity coefficients
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929468886482944 |
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| author | Wang, Shan |
| author_facet | Wang, Shan |
| contents | We consider the global well-posedness of the inhomogeneous incompressible Navier-Stokes-Korteweg system with a general capillary term. Based on the maximal regularity property, we obtain the global existence and uniqueness of solutions to the incompressible Navier-Stokes-Korteweg system with variable viscosity and capillary terms. By assuming the initial density $ρ_0$ is close to a positive constant, additionally, the initial velocity $u_0$ and the initial density $\nabla ρ_0$ are small in critical space $\dot B^{-1+d/p}_{p,1}(\mathbb R^{d})$ $(1<p<d).$ This work relies on the maximal regularity property of the heat equation, of the Stokes equation, and of the Lamé equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11675 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global existence and uniqueness of the density-dependent incompressible Navier-Stokes-Korteweg system with variable capillarity and viscosity coefficients Wang, Shan Analysis of PDEs We consider the global well-posedness of the inhomogeneous incompressible Navier-Stokes-Korteweg system with a general capillary term. Based on the maximal regularity property, we obtain the global existence and uniqueness of solutions to the incompressible Navier-Stokes-Korteweg system with variable viscosity and capillary terms. By assuming the initial density $ρ_0$ is close to a positive constant, additionally, the initial velocity $u_0$ and the initial density $\nabla ρ_0$ are small in critical space $\dot B^{-1+d/p}_{p,1}(\mathbb R^{d})$ $(1<p<d).$ This work relies on the maximal regularity property of the heat equation, of the Stokes equation, and of the Lamé equation. |
| title | Global existence and uniqueness of the density-dependent incompressible Navier-Stokes-Korteweg system with variable capillarity and viscosity coefficients |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.11675 |