Periodic Cauchy Problem for one Two-dimensional Generalization of the Benjamin-Ono Equation in Sobolev Spaces of Low Regularity

Eddye Bustamante, José Jiménez Urrea, Jorge Mejía

In this work we prove that the initial value problem (IVP) associated to the two-dimensional Benjamin-Ono equation $$\left. \begin{array}{rl} u_t+\mathcal H Δu +uu_x &\hspace{-2mm}…