论文标题
Euler-Korteweg方程和两流体的Euler-Maxwell方程的大量存在
Large time existence of Euler-Korteweg equations and two-fluid Euler-Maxwell equations with vorticity
论文作者
论文摘要
本手稿的目的是研究涡度对流体系统中存在时间的影响，在小小的无关数据的情况下，全球平滑度和衰减是已知的。我们关注两个示例：Euler-Korteweg系统和两流体Euler Maxwell系统。我们证明，这些系统的寿命的下限不低于初始速度的旋转部分的$ h^s $ $（s> 5/2）$的倒数。我们的方法基于能量估计和具有小无关初始数据的这些系统的全球解决方案的快速衰减结果。
The aim of this manuscript is to study the influence of the vorticity on the existence time in fluid systems for which global smoothness and decay is known in the case of small irrotational data. We focus on two examples: the Euler-Korteweg system and the two-fluid Euler Maxwell system. We prove that the lower bound of the lifespan of these systems is no less than the inverse of the $H^s$ $(s>5/2)$ norm of the rotational part of the initial velocity. Our approach is based on energy estimates and the fast time decay results of global solutions to these systems with small irrotational initial data.
