TY - JOUR
T1 - Remarks on the semirelativistic Hartree equations
AU - Cho, Yonggeun
AU - Ozawa, Tohru
AU - Sasaki, Hironobu
AU - Shim, Yongsun
N1 - Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.
PY - 2009/4
Y1 - 2009/4
N2 - We study the global well-posedness (GWP) and small data scattering of radial solutions of the semirelativistic Hartree type equations with nonlocal nonlinearity F(u) = λ(| · |-γ * |u| 2)u, λ ∈ ℝ \ {0}, 0 < γ < n, n ≥ 3. We establish a weighted L2 Strichartz estimate applicable to non-radial functions and some fractional integral estimates for radial functions.
AB - We study the global well-posedness (GWP) and small data scattering of radial solutions of the semirelativistic Hartree type equations with nonlocal nonlinearity F(u) = λ(| · |-γ * |u| 2)u, λ ∈ ℝ \ {0}, 0 < γ < n, n ≥ 3. We establish a weighted L2 Strichartz estimate applicable to non-radial functions and some fractional integral estimates for radial functions.
KW - Global well-posedness
KW - Radial solutions
KW - Scattering
KW - Semirelativistic hartree type equations
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U2 - 10.3934/dcds.2009.23.1277
DO - 10.3934/dcds.2009.23.1277
M3 - Article
AN - SCOPUS:62649143305
SN - 1078-0947
VL - 23
SP - 1277
EP - 1294
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 4
ER -