TY - JOUR
T1 - Remarks on nonlinear Schrödinger equations in one space dimension
AU - Hayashi, Nakao
AU - Ozawa, Tohru
AU - Bona, J. L.
PY - 1994/3
Y1 - 1994/3
N2 - We consider the initial value problem for nonlinear Schödinger equations, where ∂ = ∂x = ∂/∂x and F: C4 → C is a polynomial having neither constant nor linear terms. Without a smallness condition on the data u0, it is shown that (+) has a unique local solution in time if u0 is in H3, 0 ∩ H2, 1, where Hm, s = {f ∈ S’ ∥f∥m, s = ∥(1 + x2)s/2 (1-Δ)f∥<∞}, m, s ∈ ℝ.
AB - We consider the initial value problem for nonlinear Schödinger equations, where ∂ = ∂x = ∂/∂x and F: C4 → C is a polynomial having neither constant nor linear terms. Without a smallness condition on the data u0, it is shown that (+) has a unique local solution in time if u0 is in H3, 0 ∩ H2, 1, where Hm, s = {f ∈ S’ ∥f∥m, s = ∥(1 + x2)s/2 (1-Δ)f∥<∞}, m, s ∈ ℝ.
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M3 - Article
AN - SCOPUS:84972525950
SN - 0893-4983
VL - 7
SP - 453
EP - 461
JO - Differential and Integral Equations
JF - Differential and Integral Equations
IS - 2
ER -