TY - JOUR
T1 - Weak solvability and well-posedness of a coupled Schrödinger-Korteweg de Vries equation for capillary-gravity wave interactions
AU - Bekiranov, Daniella
AU - Ogawa, Takayoshi
AU - Ponce, Gustavo
PY - 1997
Y1 - 1997
N2 - An interaction equation of the capillary-gravity wave is considered. We show that the Cauchy problem of the coupled Schrödinger-KdV equation, (itu + x2u -αvu + γ|u|2u, x ∈ R, tv + x3 + xv2 =βx(|u|2), u(x, 0) = u0(x), v(x, 0) = v0(x), is locally well-posed for weak initial data U0 × v0 ε L2(R) × L21/2(R) × H-1/2 (R). We apply the analogous method for estimating the nonlinear coupling terms developed by Bourgain and refined by Kenig, Ponce, and Vega.
AB - An interaction equation of the capillary-gravity wave is considered. We show that the Cauchy problem of the coupled Schrödinger-KdV equation, (itu + x2u -αvu + γ|u|2u, x ∈ R, tv + x3 + xv2 =βx(|u|2), u(x, 0) = u0(x), v(x, 0) = v0(x), is locally well-posed for weak initial data U0 × v0 ε L2(R) × L21/2(R) × H-1/2 (R). We apply the analogous method for estimating the nonlinear coupling terms developed by Bourgain and refined by Kenig, Ponce, and Vega.
KW - Capillary-gravity wave
KW - Kdv
KW - Nonlinear Schrödinger
KW - Well-posedness
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U2 - 10.1090/s0002-9939-97-03941-5
DO - 10.1090/s0002-9939-97-03941-5
M3 - Article
AN - SCOPUS:21944435751
SN - 0002-9939
VL - 125
SP - 2907
EP - 2919
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 10
ER -