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

doi:10.1007/s10473-020-0313-4

Abstract

Abstract: 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 (u₀, u₁) satisfy the conditions E(u₀, u₁) < E(W, 0) and||▽u₀||₂² >||▽W||₂² for some ground state W, then the corresponding solution must blows up in finite time.

Key words: Cauchy problem, wave-hartree equation, blow up, Strichartz estimate

CLC Number:

35J10

Suxia XIA. ON BLOW-UP PHENOMENON OF THE SOLUTION TO SOME WAVE-HARTREE EQUATION IN d ≥ 5[J].Acta mathematica scientia,Series B, 2020, 40(3): 782-794.

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