论文标题
3D Euler的冲击形成和涡度创造
Shock formation and vorticity creation for 3d Euler
论文作者
论文摘要
我们分析了具有理想气体定律的3D非异源性Euler方程的冲击形成过程，其中声波与熵波相互作用以产生涡度。基于我们在[3,4]中的等渗流量理论的基础上，我们从平滑的初始数据中给出了冲击形成的建设性证明。具体而言，我们证明了对非凝集欧拉方程的平滑解决方案，该方程形成了通用稳定冲击，并明确可计算的爆炸时间，位置和方向。这是通过在调制自相似变量中建立通用冲击曲线的渐近稳定性来实现的，通过以下方式通过以下方式控制波族的相互作用：（i）沿拉格朗日轨迹沿Lagrangian轨迹的角度界限，（ii）sobolev空间中的（iii）高级能量估计值。
We analyze the shock formation process for the 3d non-isentropic Euler equations with the ideal gas law, in which sounds 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 non-isentropic 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.
