TY - JOUR
T1 - On the well-posedness of the Schrodinger-Korteweg-de Vries system
AU - Guo, Zihua
AU - Wang, Yuzhao
PY - 2010
Y1 - 2010
N2 - We prove that the Cauchy problem for the Schrodinger-Korteweg-de Vries system is locally well-posed for the initial data belonging to the Sobolev spaces L 2(R)?H -3/4(R), and H s(R)?H -3/4(R) (s>-1/16) for the resonant case. The new ingredient is that we use the F? s-type space, introduced by the first author in Guo (2009) [10], to deal with the KdV part of the system and the coupling terms. In order to overcome the difficulty caused by the lack of scaling invariance, we prove uniform estimates for the multiplier. This result improves the previous one by Corcho and Linares (2007) [6].
AB - We prove that the Cauchy problem for the Schrodinger-Korteweg-de Vries system is locally well-posed for the initial data belonging to the Sobolev spaces L 2(R)?H -3/4(R), and H s(R)?H -3/4(R) (s>-1/16) for the resonant case. The new ingredient is that we use the F? s-type space, introduced by the first author in Guo (2009) [10], to deal with the KdV part of the system and the coupling terms. In order to overcome the difficulty caused by the lack of scaling invariance, we prove uniform estimates for the multiplier. This result improves the previous one by Corcho and Linares (2007) [6].
UR - http://www.sciencedirect.com/science/article/pii/S0022039610001506/pdf?md5=7b2ee4d052908ef39d7da98dafc29e51&pid=1-s2.0-S0022039610001506-main.pdf
U2 - 10.1016/j.jde.2010.04.016
DO - 10.1016/j.jde.2010.04.016
M3 - Article
SN - 0022-0396
VL - 249
SP - 2500
EP - 2520
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 10
ER -