TY - JOUR
T1 - Local well-posedness for dispersion generalized Benjamin-Ono equations in Sobolev spaces
AU - Guo, Zihua
PY - 2012
Y1 - 2012
N2 - We prove that the Cauchy problem for the dispersion generalized Benjamin-Ono equation?tu+ ?x 1+??xu+uux=0,u(x,0)=u0(x), is locally well-posed in the Sobolev spaces H s for s>1-? if 0???1. The new ingredient is that we generalize the methods of Ionescu, Kenig and Tataru (2008) [13] to approach the problem in a less perturbative way, in spite of the ill-posedness results of Molinet, Saut and Tzvetkov (2001) [21]. Moreover, as a bi-product we prove that if 0
AB - We prove that the Cauchy problem for the dispersion generalized Benjamin-Ono equation?tu+ ?x 1+??xu+uux=0,u(x,0)=u0(x), is locally well-posed in the Sobolev spaces H s for s>1-? if 0???1. The new ingredient is that we generalize the methods of Ionescu, Kenig and Tataru (2008) [13] to approach the problem in a less perturbative way, in spite of the ill-posedness results of Molinet, Saut and Tzvetkov (2001) [21]. Moreover, as a bi-product we prove that if 0
UR - http://www.sciencedirect.com/science/article/pii/S0022039611004396/pdf?md5=899852b85d1b5973209cdffde44b0d78&pid=1-s2.0-S0022039611004396-main.pdf
U2 - 10.1016/j.jde.2011.10.012
DO - 10.1016/j.jde.2011.10.012
M3 - Article
SN - 0022-0396
VL - 252
SP - 2053
EP - 2084
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 3
ER -