Large-time behavior of solutions for unipolar Euler-Poisson equations with critical over-damping
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Bibliographic record
Abstract
This paper is concerned with the large-time behavior of solutions to the Cauchy problem for the one-dimensional unipolar Euler-Poisson equations with critical time-dependent over-damping. We prove that the Cauchy problem admits a unique global smooth solution which time-asymptotically converges to the stationary solution in the logarithmic form $ O(\ln^{-\frac{k}{2}}(1+t)) $ for the integer $ k\in[1, +\infty) $. In particular, the integer $ k $ can be large enough as the initial perturbation is small enough. This convergence rate is much better than the previous studies with critical over-damping. The proof is based on the technical time-weighted energy estimates and the mathematical induction.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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