Large-time behavior of pressureless Euler--Poisson equations with background states
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913885769957376 |
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| author | Choi, Young-Pil Kim, Dong-ha Koo, Dowan Tadmor, Eitan |
| author_facet | Choi, Young-Pil Kim, Dong-ha Koo, Dowan Tadmor, Eitan |
| contents | We study the large-time asymptotic behavior of solutions to the one-dimensional damped pressureless Euler-Poisson system with variable background states, subject to a neutrality condition. In the case where the background density converges asymptotically to a positive constant, we establish the convergence of global classical solutions toward the corresponding equilibrium state. The proof combines phase plane analysis with hypocoercivity-type estimates. As an application, we analyze the damped pressureless Euler--Poisson system arising in cold plasma ion dynamics, where the electron density is modeled by a Maxwell-Boltzmann relation. We show that solutions converge exponentially to the steady state under suitable a priori bounds on the density and velocity fields. Our results provide a rigorous characterization of asymptotic stability for damped Euler-Poisson systems with nontrivial background structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07812 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large-time behavior of pressureless Euler--Poisson equations with background states Choi, Young-Pil Kim, Dong-ha Koo, Dowan Tadmor, Eitan Analysis of PDEs Primary 35Q35, Secondary 35B40 We study the large-time asymptotic behavior of solutions to the one-dimensional damped pressureless Euler-Poisson system with variable background states, subject to a neutrality condition. In the case where the background density converges asymptotically to a positive constant, we establish the convergence of global classical solutions toward the corresponding equilibrium state. The proof combines phase plane analysis with hypocoercivity-type estimates. As an application, we analyze the damped pressureless Euler--Poisson system arising in cold plasma ion dynamics, where the electron density is modeled by a Maxwell-Boltzmann relation. We show that solutions converge exponentially to the steady state under suitable a priori bounds on the density and velocity fields. Our results provide a rigorous characterization of asymptotic stability for damped Euler-Poisson systems with nontrivial background structures. |
| title | Large-time behavior of pressureless Euler--Poisson equations with background states |
| topic | Analysis of PDEs Primary 35Q35, Secondary 35B40 |
| url | https://arxiv.org/abs/2506.07812 |