TY - JOUR
T1 - Analytic smoothing effects of global small solutions to the elliptic-hyperbolic davey-stewartson system
AU - Hayashi, Nakao
AU - Naumkin, Pavel I.
AU - Uchida, Hidetake
PY - 2002/12/1
Y1 - 2002/12/1
N2 - We study the elliptic-hyperbolic Davey-Stewartson system , where c1, c2 ∈ R, u is a complex valued function and φ is a real valued function. The system can be translated to nonlocal nonlinear Schrödinger equations after a rotation and a rescaling, where c0, c1, c2 ∈ C. Our purpose in this paper is to prove that if the norm ||(π2j=1 cosh θxj)u0||3,0 + ||(π2j=1 cosh θxj)u0||0,3 for θ ≠ 0 is sufficiently small, then small solutions of (NLS) exist and become analytic with respect to x for any t ≠ 0 . Here we denote the weighted Sobolev space by Hm,s = {φ ∈ L2; ||φ||m,s =(1+x21+x22)s/2(1-∂2x1-∂2x2)m/2φ|| < infin; }, m, s ∈ R+.
AB - We study the elliptic-hyperbolic Davey-Stewartson system , where c1, c2 ∈ R, u is a complex valued function and φ is a real valued function. The system can be translated to nonlocal nonlinear Schrödinger equations after a rotation and a rescaling, where c0, c1, c2 ∈ C. Our purpose in this paper is to prove that if the norm ||(π2j=1 cosh θxj)u0||3,0 + ||(π2j=1 cosh θxj)u0||0,3 for θ ≠ 0 is sufficiently small, then small solutions of (NLS) exist and become analytic with respect to x for any t ≠ 0 . Here we denote the weighted Sobolev space by Hm,s = {φ ∈ L2; ||φ||m,s =(1+x21+x22)s/2(1-∂2x1-∂2x2)m/2φ|| < infin; }, m, s ∈ R+.
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M3 - Article
AN - SCOPUS:14944381777
SN - 1079-9389
VL - 7
SP - 469
EP - 492
JO - Advances in Differential Equations
JF - Advances in Differential Equations
IS - 4
ER -