AI 中文总结
研究一维及多维径向对称的排斥性欧拉-泊松方程，假设幂律速度依赖阻尼系数，发现一维中对应全局光滑解的初值集扩展，其他维度（除4维）阻尼不改善解的光滑性，稳态小扰动会爆破。
AI 中文摘要
我们考虑一维空间以及具有径向对称性的多维情况下的排斥性欧拉-泊松方程，假设阻尼系数为幂律速度依赖型。结果表明，在此假设下，一维情形中对应全局时间光滑解的初始数据集会扩展，而在其他维度（除4维外），阻尼对解的光滑性改善无影响，即稳态的任意小扰动都会爆破，尽管其振荡幅度会衰减。
英文摘要
We consider repulsive Euler-Poisson equations in both one-dimensional space and in the multidimensional case with radial symmetry, assuming a power-law velocity-dependent damping coefficient. We show that under this assumption, in the one-dimensional case the set of initial data corresponding to a globally time-smooth solution expands, whereas in other dimensions (except for dimension 4) the damping does not influence on improving of smooth properties of the solution. Namely, any arbitrary small perturbation of the steady state blow up, despite of its amplitude of oscillations decays.
Comments15 pages, 4 figures
