论文标题
可压缩欧拉方程的真空和奇异性形成与时间相关阻尼
Vacuum and singularity formation for compressible Euler equations with time-dependent damping
论文作者
论文摘要
在本文中，对于可压缩的欧拉方程而言，真空和奇异性形成与时间相关的阻尼被认为。对于$ 1 <γ\ leq 3 $，通过巧妙地构建一些新的控制功能，我们可以获得对任意经典解决方案密度的下限估计值。根据这些较低的估计，我们成功地证明了所有$λ$的奇异形式定理，在某些情况下，它在[1]中开放。此外，当研究$γ= 3 $时，可压缩欧拉方程的奇异性形成也是如此。
In this paper, vacuum and singularity formation are considered for compressible Euler equations with time-dependent damping. For $1<γ\leq 3$, by constructing some new control functions ingeniously, we obtain the lower bounds estimates on density for arbitrary classical solutions. Basing on these lower estimates, we succeed in proving the singular formation theorem for all $λ$, which was open in [1] for some cases.Moreover, the singularity formation of the compressible Euler equations when $γ=3$ is investigated, too.
