ON BLOW-UP PHENOMENON OF THE SOLUTION TO SOME WAVE-HARTREE EQUATION IN d≥5

This article mainly considers the blow up phenomenon of the solution to the wave-hartree equation u_(tt)-?u =(|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(u_0, u_1) satisfy the conditions E(u_0, u_1) E(W, 0) and ||?u0||_2~2 ||?W|| _2~2 for some ground state W, then the corresponding solution must blows up in finite time.