TY - JOUR
T1 - On scattering for the defocusing high dimensional inter-critical NLS
AU - Gao, Chuanwei
AU - Zhao, Zehua
N1 - Publisher Copyright:
© 2019 Elsevier Inc.
PY - 2019/11/15
Y1 - 2019/11/15
N2 - In this paper, we study the critical norm conjecture for the inter-critical nonlinear Schrödinger equation with critical index sc satisfying [Formula presented] c<1 when d≥5. Under the assumption of uniform boundedness of the critical norm, we prove the global well-posedness and scattering for the Cauchy problem. We follow the standard ‘Concentration compactness/Rigidity method’ established in [15,16], and treat three scenarios for the critical element respectively. Moreover, double Duhamel method and interaction Morawetz estimate are applied to exclude the critical element.
AB - In this paper, we study the critical norm conjecture for the inter-critical nonlinear Schrödinger equation with critical index sc satisfying [Formula presented] c<1 when d≥5. Under the assumption of uniform boundedness of the critical norm, we prove the global well-posedness and scattering for the Cauchy problem. We follow the standard ‘Concentration compactness/Rigidity method’ established in [15,16], and treat three scenarios for the critical element respectively. Moreover, double Duhamel method and interaction Morawetz estimate are applied to exclude the critical element.
UR - https://www.scopus.com/pages/publications/85067958892
U2 - 10.1016/j.jde.2019.06.019
DO - 10.1016/j.jde.2019.06.019
M3 - Article
AN - SCOPUS:85067958892
SN - 0022-0396
VL - 267
SP - 6198
EP - 6215
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 11
ER -