Nonlinear Stability of the Rayleigh-Taylor Problem in Quantum Navier-Stokes Equations
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914082342305792 |
|---|---|
| author | Jiang, Fei Zhang, Yajie Zhang, Zhipeng Zhao, Youyi |
| author_facet | Jiang, Fei Zhang, Yajie Zhang, Zhipeng Zhao, Youyi |
| contents | It is well-known that the Rayleigh--Taylor (abbr. RT) instability can be completely inhibited by the quantum effect stabilization in proper circumstances leading to a cutoff wavelength in the \emph{linear} motion equations. Motivated by the linear theory, we further investigate the {stability} for the \emph{nonlinear} RT problem of quantum Navier--Stokes equations in a slab with Navier boundary condition, and rigorously prove the inhibition of RT instability by the quantum effect under a proper setting. More precisely, if the RT density profile $\barρ$ satisfies an additional stabilizing condition, then there is a threshold ${\varepsilon_{c}}$ of the scaled Planck constant, such that if the scaled Planck constant is bigger than ${\varepsilon_{c}}$, the small perturbation solutions around an RT equilibrium state are algebraically stable in time. The mathematical proof is realized by a complicated multi-layer energy method with anisotropic norms of spacial derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07695 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonlinear Stability of the Rayleigh-Taylor Problem in Quantum Navier-Stokes Equations Jiang, Fei Zhang, Yajie Zhang, Zhipeng Zhao, Youyi Analysis of PDEs 35Q35, 76D03, 76E99 It is well-known that the Rayleigh--Taylor (abbr. RT) instability can be completely inhibited by the quantum effect stabilization in proper circumstances leading to a cutoff wavelength in the \emph{linear} motion equations. Motivated by the linear theory, we further investigate the {stability} for the \emph{nonlinear} RT problem of quantum Navier--Stokes equations in a slab with Navier boundary condition, and rigorously prove the inhibition of RT instability by the quantum effect under a proper setting. More precisely, if the RT density profile $\barρ$ satisfies an additional stabilizing condition, then there is a threshold ${\varepsilon_{c}}$ of the scaled Planck constant, such that if the scaled Planck constant is bigger than ${\varepsilon_{c}}$, the small perturbation solutions around an RT equilibrium state are algebraically stable in time. The mathematical proof is realized by a complicated multi-layer energy method with anisotropic norms of spacial derivatives. |
| title | Nonlinear Stability of the Rayleigh-Taylor Problem in Quantum Navier-Stokes Equations |
| topic | Analysis of PDEs 35Q35, 76D03, 76E99 |
| url | https://arxiv.org/abs/2510.07695 |