论文标题
2D等性压缩欧拉的不稳定冲击形成
Formation of unstable shocks for 2D isentropic compressible Euler
论文作者
论文摘要
在本文中，我们在方位角对称性中的2D等粒子可压缩欧拉的背景下构建了不稳定的冲击。更具体地说，我们构建了初始数据，当在自相似坐标中查看时，将渐近收敛到不稳定的$ c^{\ frac15} $自相似于汉堡方程的解决方案。此外，我们在$ c^8 $ modulo中表明行为是稳定的，一个二维线性子空间。在方位角对称假设下，为了隔离导致稳定性的初始数据的相应歧管，不能施加其他对称性假设：相反，我们依靠调制变量技术与牛顿方案结合使用。
In this paper we construct unstable shocks in the context of 2D isentropic compressible Euler in azimuthal symmetry. More specifically, we construct initial data that when viewed in self-similar coordinates, converges asymptotically to the unstable $C^{\frac15}$ self-similar solution to the Burgers' equation. Moreover, we show the behavior is stable in $C^8$ modulo a two dimensional linear subspace. Under the azimuthal symmetry assumption, one cannot impose additional symmetry assumptions in order to isolate the corresponding manifold of initial data leading to stability: rather, we rely on modulation variable techniques in conjunction with a Newton scheme.
