论文标题
双曲线系统中的尖锐临界阈值
Sharp critical thresholds in a hyperbolic system with relaxation
论文作者
论文摘要
我们建议并研究一个一维$ 2 \ times 2 $双曲线欧拉系统，从临界阈值现象的角度来看，局部放松。该系统具有严格和弱双曲线之间的动态过渡。对于不同类别的放松，我们确定了固有的临界阈值，以区分全球规则性和有限时间爆炸的初始数据。对于与密度无关的松弛，我们在系统严格双曲线的情况下以速度估计密度的界限。
We propose and study a one-dimensional $2\times 2$ hyperbolic Eulerian system with local relaxation from critical threshold phenomena perspective. The system features dynamic transition between strictly and weakly hyperbolic. For different classes of relaxation we identify intrinsic critical thresholds for initial data that distinguish global regularity and finite time blowup. For relaxation independent of density, we estimate bounds on density in terms of velocity where the system is strictly hyperbolic.
