TY - CHAP
T1 - On the focusing energy-critical 3d quintic inhomogeneous nls
AU - Cho, Yonggeun
AU - Lee, Kiyeon
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - We consider the focusing energy-critical inhomogeneous nonlinear Schrödinger equation: iut+Δu+g|u|4u=0,u(0)∈Ḣ1,g≥0. $$\displaystyle iu_t + \Delta u + g|u|{ }^4u = 0, \;\;u(0) \in \dot {H}^1,\;\; g \ge 0. $$ On the road map of Kenig–Merle [20] we show the global well-posedness and scattering of radial solutions under scaling, variational, and rigidity assumptions for g. We also provide sharp finite time blowup results for nonradial and radial solutions. For this we utilize the localized virial identity.
AB - We consider the focusing energy-critical inhomogeneous nonlinear Schrödinger equation: iut+Δu+g|u|4u=0,u(0)∈Ḣ1,g≥0. $$\displaystyle iu_t + \Delta u + g|u|{ }^4u = 0, \;\;u(0) \in \dot {H}^1,\;\; g \ge 0. $$ On the road map of Kenig–Merle [20] we show the global well-posedness and scattering of radial solutions under scaling, variational, and rigidity assumptions for g. We also provide sharp finite time blowup results for nonradial and radial solutions. For this we utilize the localized virial identity.
KW - Bounded inhomogeneous coefficient
KW - Energy-critical NLS
KW - Focusing
KW - Global well-posedness
KW - Kenig-Merle argument
UR - https://www.scopus.com/pages/publications/85095853809
U2 - 10.1007/978-3-030-58215-9_6
DO - 10.1007/978-3-030-58215-9_6
M3 - Chapter
AN - SCOPUS:85095853809
T3 - Trends in Mathematics
SP - 165
EP - 195
BT - Trends in Mathematics
PB - Springer Science and Business Media Deutschland GmbH
ER -