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.

UR - http://www.scopus.com/inward/record.url?scp=33747836758&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33747836758&partnerID=8YFLogxK

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 -