Nunes, Wagner V. L. On the well-posedness and scattering for the transitional Benjamin-Ono equation. (English) Zbl 0854.35105 Mat. Contemp. 3, 127-148 (1992). We consider the Cauchy problem for the transitional Benjamin-Ono equation \[ \partial_t u+ \sigma \partial^2_x u+ f(t) u\partial_x u= 0,\quad u(t_0, x)= \phi(x),\tag{1} \] where \(\sigma\) is the Hilbert transform, i.e., \((\sigma\varphi) (x)=(1/\pi)\) p.v. \(\int_{\mathbb{R}} {\varphi(y)\over y- x} dy\).Our purpose is to investigate the local and the global well-posedness of the problem (1) in the Sobolev spaces \(H^s(R)\), when \(s\geq 3/2\). Cited in 4 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35A07 Local existence and uniqueness theorems (PDE) (MSC2000) Keywords:local well-posedness; almost conserved quantities; asymptotic behavior; scattering; Cauchy problem; Benjamin-Ono equation; global well-posedness PDFBibTeX XMLCite \textit{W. V. L. Nunes}, Mat. Contemp. 3, 127--148 (1992; Zbl 0854.35105)