TY - JOUR
T1 - Domain and range of the modified wave operator for schrödinger equations with a critical nonlinearity
AU - Hayashi, Nakao
AU - Naumkin, Pavel I.
PY - 2006/10
Y1 - 2006/10
N2 - We study the final problem for the nonlinear Schrödinger equation itu+ 1/2 Δu = λ|u|2/nu, (t,x)∈ R × Rn where λ ∈ R,n =1,2,3. If the final data u + ∈ H0,α = {φ ∈ L2 :( 1+|x|)α φ ∈ L2}with n/2 < α < min( n, 2,1+2/n) and the norm ∥û+∥L ∞t is sufficiently small, then we prove the existence of the wave operator in L 2. We also construct the modified scattering operator from H 0,α to H 0,δ with n/2 < δ < α.
AB - We study the final problem for the nonlinear Schrödinger equation itu+ 1/2 Δu = λ|u|2/nu, (t,x)∈ R × Rn where λ ∈ R,n =1,2,3. If the final data u + ∈ H0,α = {φ ∈ L2 :( 1+|x|)α φ ∈ L2}with n/2 < α < min( n, 2,1+2/n) and the norm ∥û+∥L ∞t is sufficiently small, then we prove the existence of the wave operator in L 2. We also construct the modified scattering operator from H 0,α to H 0,δ with n/2 < δ < α.
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U2 - 10.1007/s00220-006-0057-6
DO - 10.1007/s00220-006-0057-6
M3 - Article
AN - SCOPUS:33747836758
SN - 0010-3616
VL - 267
SP - 477
EP - 492
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -