This article mainly considers the blow up phenomenon of the solution to the wave-hartree equation u_tt − Δu = (|x|⁻⁴ * |u|²)u in the energy space for high dimensions d ≥ 5. The main result of this article is that: if the initial data (u₀, u₁) satisfy the conditions E(u₀, u₁) < E(W, 0) and \(\parallel\triangledown{u_0}\parallel_2^2>\parallel\triangledown{W}\parallel_2^2\) for some ground state W, then the corresponding solution must blows up in finite time.

中文翻译：

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d≥5时一类波动方程的解的爆破现象。

本文主要考虑吹胀该溶液到波哈特里方程的现象ü _TT - Δ û =（| X | ^-4 * | U | ²）Ü在高维的能量空间ð ≥5.主要结果本文的内容是：如果初始数据（u ₀，u ₁）满足条件E（u ₀，u ₁）< E（W，0）和\（\ parallel \ triangledown {u_0} \ parallel_2 ^ 2> \ parallel \ triangledown {W} \ parallel_2 ^ 2 \）对于某些基态W，则相应的解必须在有限的时间内爆炸。