论文标题
3D可压缩欧拉方程的偏移冲击形成潮湿
Formation of shifted shock for the 3D compressible Euler equations with damping
论文作者
论文摘要
在本文中，我们显示了溶液对3维（3D）可压缩的等粒子和无旋Euler方程的冲击形成，并对初始短脉冲数据进行了阻尼，这是D.Christodoulou \ cite {ChristoDoulou2007}首先引入的。由于阻尼效应，对冲击形成的初始数据的宽敞性是必不可少的，我们将处理大数据类别（在能源意义上）。与未阻尼的情况相似，冲击的形成的特征是特征性突出的崩溃和反向叶片密度函数的消失$μ$，速度的第一个衍生物和密度的第一个衍生物膨胀。然而，阻尼效应改变了反叶密度函数的渐近行为$μ$，然后与未阻尼情况相比会改变冲击形成时间。本文中的方法还可以扩展到短脉冲初始数据的$ 3D $ quasilinear Wave方程。
In this paper, we show the shock formation of the solutions to the 3-dimensional (3D) compressible isentropic and irrotational Euler equations with damping for the initial short pulse data which was first introduced by D.Christodoulou\cite{christodoulou2007}. Due to the damping effect, the largeness of the initial data is necessary for the shock formation and we will work on the class of large data (in energy sense). Similar to the undamped case, the formation of shock is characterized by the collapse of the characteristic hypersurfaces and the vanishing of the inverse foliation density function $μ$, at which the first derivatives of the velocity and the density blow up. However, the damping effect changes the asymptotic behavior of the inverse foliation density function $μ$ and then shifts the time of shock formation compared with the undamped case. The methods in the paper can also be extended to a class of $3D$ quasilinear wave equations for the short pulse initial data.
