Formation of Unstable Shocks for 2D Isentropic Compressible Euler
Formation of Unstable Shocks for 2D Isentropic Compressible Euler
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DOI：
10.1007/s00220-021-04271-z
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发表时间：
2020-07
影响因子：
2.4
通讯作者：
T. Buckmaster;Sameer Iyer
中科院分区：
文献类型：
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作者：
T. Buckmaster;Sameer Iyer
本文在二维等熵可压缩欧拉方程中构造了方位对称的不稳定激波。更具体地说，我们构造初始数据，当在自相似坐标下观察时，渐近收敛到Burgers方程的不稳定自相似解。此外，我们还证明了该行为在模二维线性子空间中是稳定的。在方位角对称假设下，不能强加额外的对称假设，以隔离相应的初始数据的流形，从而获得稳定性：相反，我们依赖于调制变量技术结合牛顿方案。
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 unstableself-similar solution to the Burgers’ equation. Moreover, we show the behavior is stable inmodulo 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.