Enhanced dissipation and temporal decay in the Euler-Poisson-Navier-Stokes equations
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910460923609088 |
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| author | Choi, Young-Pil Tang, Houzhi Zou, Weiyuan |
| author_facet | Choi, Young-Pil Tang, Houzhi Zou, Weiyuan |
| contents | This paper investigates the global well-posedness and large-time behavior of solutions for a coupled fluid model in $\mathbb{R}^3$ consisting of the isothermal compressible Euler-Poisson system and incompressible Navier-Stokes equations coupled through the drag force. Notably, we exploit the dissipation effects inherent in the Poisson equation to achieve a faster decay of fluid density compared to velocities. This strategic utilization of dissipation, together with the influence of the electric field and the damping structure induced by the drag force, leads to a remarkable decay behavior: the fluid density converges to equilibrium at a rate of $(1+t)^{-11/4}$, significantly faster than the decay rates of velocity differences $(1+t)^{-7/4}$ and velocities themselves $(1+t)^{-3/4}$ in the $L^2$ norm. Furthermore, under the condition of vanishing coupled incompressible flow, we demonstrate an exponential decay to a constant state for the solution of the corresponding system, the damped Euler-Poisson system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17895 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enhanced dissipation and temporal decay in the Euler-Poisson-Navier-Stokes equations Choi, Young-Pil Tang, Houzhi Zou, Weiyuan Analysis of PDEs 35B40, 35B65, 76N10 This paper investigates the global well-posedness and large-time behavior of solutions for a coupled fluid model in $\mathbb{R}^3$ consisting of the isothermal compressible Euler-Poisson system and incompressible Navier-Stokes equations coupled through the drag force. Notably, we exploit the dissipation effects inherent in the Poisson equation to achieve a faster decay of fluid density compared to velocities. This strategic utilization of dissipation, together with the influence of the electric field and the damping structure induced by the drag force, leads to a remarkable decay behavior: the fluid density converges to equilibrium at a rate of $(1+t)^{-11/4}$, significantly faster than the decay rates of velocity differences $(1+t)^{-7/4}$ and velocities themselves $(1+t)^{-3/4}$ in the $L^2$ norm. Furthermore, under the condition of vanishing coupled incompressible flow, we demonstrate an exponential decay to a constant state for the solution of the corresponding system, the damped Euler-Poisson system. |
| title | Enhanced dissipation and temporal decay in the Euler-Poisson-Navier-Stokes equations |
| topic | Analysis of PDEs 35B40, 35B65, 76N10 |
| url | https://arxiv.org/abs/2405.17895 |