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On the Cauchy problem of a two-dimesional Benjamin-Ono equation (1503.04290v1)
Published 14 Mar 2015 in math.AP
Abstract: In this work we shall show that the Cauchy problem \begin{equation} \left{ \begin{aligned} &(u_t+upu_x+\mathcal H\partial_x2u+ \alpha\mathcal H\partial_y2u )x - \gamma u{yy}=0 \quad p\in{\nat} &u(0;x,y)=\phi{(x,y)} \end{aligned} \right. \end{equation} is locally well-posed in the Sobolev spaces $Hs({\re}2)$, $Xs$ and weighted spaces $X_s(w2)$, for $s>2$.