论文标题
等离子体离子动力学中奇异性的形成
Formation of Singularities in Plasma Ion Dynamics
论文作者
论文摘要
我们研究了配备有玻尔兹曼关系的Euler-Poisson系统的奇异性的形成，该系统描述了静电等离子体中离子的动力学。通常，众所周知，非线性双曲线方程的平滑溶液在全球范围内无法及时存在。我们建立了$ c^1 $ blower的欧拉 - 波森系统的标准，包括等温线和无压力案例。特别是，我们对无预售模型的爆炸条件并不要求速度的梯度较大。实际上，我们的结果特别意味着即使初始速度的梯度微不足道，平滑溶液也会分解。对于等温案例，我们证明平滑的解决方案在最初的Riemann功能梯度最大时会在有限的时间内留下$ C^1 $类。
We study the formation of singularity for the Euler-Poisson system equipped with the Boltzmann relation, which describes the dynamics of ions in an electrostatic plasma. In general, it is known that smooth solutions to nonlinear hyperbolic equations fail to exist globally in time. We establish criteria for $C^1$ blow-up of the Euler-Poisson system, both for the isothermal and pressureless cases. In particular, our blow-up condition for the presureless model does not require that the gradient of velocity is negatively large. In fact, our result particularly implies that the smooth solutions can break down even if the gradient of initial velocity is trivial. For the isothermal case, we prove that smooth solutions leave $C^1$ class in a finite time when the gradients of the Riemann functions are initially large.
