On a higher dimensional version of the Benjamin--Ono equation

Felipe Linares, Oscar G. Riaño, Keith M. Rogers +2

We consider a higher dimensional version of the Benjamin--Ono equation, ${\partial }_{t}u-{\mathcal{R}}_1\Delta u+u{\partial }_{x_1}u=0$, where ${\mathcal{R}}_1$ denotes the Riesz transform with…