关于三维Euler方程自相似解的Luo-Hou方法的进一步注记
Further remarks on the Luo-Hou's ansatz for a self-similar solution to the 3D Euler equations
摘要：
结果表明，T. Hou和G. Luo描述了三维轴对称Euler方程的奇异解，在不假设自相似轮廓的任何渐近条件的情况下，导致产生两族解的超定偏微分方程偏微分方程组：一类平凡解，其中涡量场为零，以及一族解立即爆破，其中涡量场由定常状态控制。在任何情况下，这些解的解析性质与T。Hou和G.罗因此，这个结果是对D. Chae和T.- P. Tsai在这一问题上，其中作者发现了在爆破剖面的某种衰减条件下的平凡解类。
英文摘要：
It is shown that the self-similar ansatz proposed by T. Hou and G. Luo to describe a singular solution of the 3D axisymmetric Euler equations leads, without assuming any asymptotic condition on the self-similar profiles, to an over-determined system of partial differential equations that produces two families of solutions: a class of trivial solutions in which the vorticity field is identically zero, and a family of solutions that blow-up immediately, where the vorticity field is governed by a stationary regime. In any case, the analytical properties of these solutions are not consistent with the numerical observations reported by T. Hou and G. Luo. Therefore, this result is a refinement of the previous work published by D. Chae and T.-P. Tsai on this matter, where the authors found the trivial class of solutions under a certain decay condition of the blow-up profiles.
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