MR2108679 Naoyasu KITA and Jun-ichi SEGATA Naoyasu KITA and Jun-ichi SEGATA Well-Posedness for the Boussinesq-Type System Related to the Water Wave Funkcialaj Ekvacioj. Serio Internacia 47 2004 329--350 http://fe.math.kobe-u.ac.jp/FE/FullPapers/47-2/47_329.pdf http://www.ams.org/mathscinet-getitem?mr=MR2108679 This paper studies the initial value problem of Boussinesq-type system which describes the motion of water waves. We show the time local well-posedness in the weighted Sobolev space. This is the generalization of Angulo's work [1] from the view of regularity. Our argument is based on the contraction mapping principle for the integral equations after reducing our problem into the derivative nonlinear Schrödinger system. To overcome the regularity loss in the nonlinearity, we shall apply the smoothing effects of linear Schrödinger group due to Kenig-Ponce-Vega [7]. The gauge transform is also used to remove size restriction on the initial data. Time local well-posedness, Derivative nonlinear Schrödinger equations, Smoothing effect, Gauge transform. 35B35. 47-329 2004 Well-Posedness for the Boussinesq-Type System Related to the Water Wave Naoyasu KITA and Jun-ichi SEGATA Naoyasu KITA and Jun-ichi SEGATA
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