Energy concentration of the focusing energy-critical fNLS

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• 作者：Yonggeun Cho^a ; ^{changocho@jbnu.ac.kr" class="auth_mail" title="E-mail the corresponding author} ; Gyeongha Hwang^b ; ^{ghhwang@ncts.ntu.edu.tw" class="auth_mail" title="E-mail the corresponding author} ; Yong-Sun Shim^c ; ^{shim@postech.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Global well-posedness ; Blowup ; Energy concentration ; Focusing energy-critical fNLS ; Concentration compactness ; Energy trapping
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：437
• 期：1
• 页码：310-329
• 全文大小：442 K

文摘

We consider the fractional nonlinear Schrödinger equation (fNLS) with non-local dispersion |∇|^α${|\mathrm{\nabla }|}^{\alpha }$ and focusing energy-critical Hartree type nonlinearity [−(|x|^−2α⁎|u|²)u]$[-({|x|}^{-2\alpha }⁎{|u|}^2)u]$. We consider the energy-concentration phenomena of radial blowup solutions near the maximal existence time. We use the concentration-compactness approach of [19] for confined case and kinetic energy trapping approach of [21] for unconfined case.