双极Euler-Poisson系统（其中一种流体无压力且无阻尼）的全局存在性与时间衰减
Global existence and time decay for a bipolar Euler-Poisson system with one pressureless and undamped fluid
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中文总结 AI 辅助
本文研究三维双极Euler-Poisson系统，在一种流体无压力且无阻尼的非对称情形下，通过精细Green函数估计与高低频分解，证明了小扰动光滑解的全局存在性、唯一性及代数时间衰减。
中文摘要 AI 辅助
我们研究三维双极Euler-Poisson系统的Cauchy问题，其中一种流体无压力且无阻尼，而另一种流体受动量松弛作用。对于常平衡态的足够小的光滑扰动，我们在无压力流体初始速度的无旋假设下，证明了光滑解的全局存在性与唯一性，并给出了代数时间衰减估计。主要困难在于无压力流体的速度仅通过Poisson耦合间接耗散，且该机制在高频处强烈退化，导致正则性损失结构。我们通过结合精细的Green函数估计、低-中-高频分解以及适应非对称正则性层次的高阶非线性能量估计来克服这一困难。该结果为此非对称情形建立了全局小数据理论，其中压力和阻尼同时在同一流体中缺失。
英文摘要
We study the Cauchy problem for a three-dimensional bipolar Euler--Poisson system in which one fluid is pressureless and undamped, while the other is subject to momentum relaxation. For sufficiently small smooth perturbations of a constant equilibrium, we prove the global existence and uniqueness of smooth solutions under an irrotationality assumption on the initial velocity of the pressureless fluid, together with algebraic time-decay estimates. The main difficulty is that the velocity of the pressureless fluid is dissipated only indirectly through the Poisson coupling, and this mechanism degenerates strongly at high frequencies, leading to a regularity-loss structure. We overcome this difficulty by combining refined Green-function estimates, a low--middle--high frequency decomposition, and high-order nonlinear energy estimates adapted to the asymmetric regularity hierarchy. The result establishes a global small-data theory for this asymmetric regime, in which pressure and damping are simultaneously absent from the same fluid.
发表机构
- Yonsei University（延世大学）
- Anhui Normal University（安徽师范大学）
- Beijing University of Chemical Technology（北京化工大学）
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