TY  - JOUR
ID  - Han2012
LB  - Han2012
AU  - Han, Pigong
TI  - Global well-posedness and scattering for the focusing nonlinear Schrödinger equation in the nonradial case
ST  - Global well-posedness and scattering for the focusing nonlinear Schrödinger equation in the nonradial case
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 3
SP  - 487
EP  - 504
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.3.487
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.3.487
AB  - The energy-critical, focusing nonlinear Schrödinger equation in the nonradial case reads as follows: \[i\partial_t u = -\Delta u -|u|^{\frac{4}{N-2}}u,\quad (x,0)=u_0 \in H^1 (\mathbb{R}^N),\quad N\geq 3.\] Under a suitable assumption on the maximal strong solution, using a compactness argument and a virial identity, we establish the global well-posedness and scattering in the nonradial case, which gives a positive answer to one open problem proposed by Kenig and Merle [Invent. Math. 166 (2006), 645–675].
KW  - critical energy
KW  - focusing Schrödinger equation
KW  - global well-posedness
KW  - scattering
SN  - 1232-9274
ER  -