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

doi:10.1007/s10473-020-0313-4

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (3): 782-794.doi: 10.1007/s10473-020-0313-4

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

夏素霞

College of Science, Henan University of Technology, Henan 450001, China

收稿日期:2019-01-06 修回日期:2019-07-02 出版日期:2020-06-25 发布日期:2020-07-17
作者简介:Suxia XIA,E-mail:xsx0122@126.com
基金资助:
This work is supported by National Natural Science Foundation of China (11601122 and 11326137).

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

Suxia XIA

College of Science, Henan University of Technology, Henan 450001, China

Received:2019-01-06 Revised:2019-07-02 Online:2020-06-25 Published:2020-07-17
Supported by:
This work is supported by National Natural Science Foundation of China (11601122 and 11326137).

摘要/Abstract

摘要： 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.

关键词: Cauchy problem, wave-hartree equation, blow up, Strichartz estimate

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

中图分类号:

35J10

夏素霞. ON BLOW-UP PHENOMENON OF THE SOLUTION TO SOME WAVE-HARTREE EQUATION IN d ≥ 5[J]. 数学物理学报(英文版), 2020, 40(3): 782-794.

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

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

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