ON THE LOCAL WELL-POSEDNESS OF A BIDIMENSIONAL
VERSION OF THE BENJAMIN-ONO EQUATION
Germán Preciado
Department of Mathematics
Universidad Nacional de Colombia
Kra. 30 No. 45-03, Oficina 334, Bogotá, D.C., COLOMBIA
Abstract. In this paper we show that the Cauchy problem \begin{equation*} \left\{ \begin{aligned} &u_t+\mathcal H^{(y)}\partial_x^2u+... ...ad p\in{\nat}, \\ &u(0)=\phi{(x,y)} \end{aligned} \right. \end{equation*} is locally well-posed in the Sobolev space $H^s({\re}^2)$, for $s>2$ and that as in the case of the BO (Benjamin-Ono) equation, there is a lack of persistence in $X^s$.
AMS Subject classification: 35K57, 35B40
Keywords and phrases: Cauchy problem, Hilbert transformation, Benjamin-Ono equation, local well-posedness


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DOI: 10.12732/ijam.v26i6.1

Volume: 26
Issue: 6
Year: 2013