Shock Formation and Vorticity Creation for 3d Euler
Shock Formation and Vorticity Creation for 3d Euler
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DOI：
10.1002/cpa.22067
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发表时间：
2020-06
影响因子：
3
通讯作者：
T. Buckmaster;S. Shkoller;V. Vicol
中科院分区：
文献类型：
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作者：
T. Buckmaster;S. Shkoller;V. Vicol
我们分析了具有理想气体定律的3D非凝集器方程的冲击形成过程，其中声波与熵波相互作用以产生涡旋，以[3，4]的理论构建。从平滑的初始数据中进行冲击。这是通过在调制的自同性变量中建立通用冲击曲线的不对称稳定性来实现的，通过以下方式控制波族的相互作用：（i）沿拉格朗日轨迹沿拉格朗日轨迹的角度，（ii）几何涡度结构，以及（iii）高级旋转轨迹。 Sobolev空间中的订单能量估计。
We analyze the shock formation process for the 3D nonisentropic Euler equations with the ideal gas law, in which sound waves interact with entropy waves to produce vorticity. Building on our theory for isentropic flows in [3, 4], we give a constructive proof of shock formation from smooth initial data. Specifically, we prove that there exist smooth solutions to the nonisentropic Euler equations which form a generic stable shock with explicitly computable blowup time, location, and direction. This is achieved by establishing the asymptotic stability of a generic shock profile in modulated self‐similar variables, controlling the interaction of wave families via: (i) pointwise bounds along Lagrangian trajectories, (ii) geometric vorticity structure, and (iii) high‐order energy estimates in Sobolev spaces. © 2022 Wiley Periodicals LLC.