4 papers
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 $$\left. \begin{array}{rl} u_t+\mathcal H Δu +uu_x &\hspace{-2mm}…
The Cauchy problem for a family of two-dimensional fractional Benjamin-Ono equations
Eddye Bustamante, José Jiménez Urrea, Jorge Mejía
In this work we prove that the initial value problem (IVP) associated to the fractional two-dimensional Benjamin-Ono equation $$\left. \begin{array}{rl} u_t+D_x^α u_x +\mathcal Hu_…
On the unique continuation property of solutions of the three-dimensional Zakharov-Kuznetsov equation
Eddye Bustamante, José Jiménez Urrea, Jorge Mejía
We prove that if the difference of two sufficiently smooth solutions of the three-dimensional Zakharov-Kuznetsov equation $$\partial_{t}u+\partial_{x}\triangle u+u\partial_{x}u=0 \…
A note on the Ostrovsky equation in weighted Sobolev spaces
Eddye Bustamante, José Jiménez Urrea, Jorge Mejía
In this work we consider the initial value problem (IVP) associated to the Ostrovsky equations $$\left. \begin{array}{rl} u_t+\partial_x^3 u\pm \partial_x^{-1}u +u \partial_x u &\h…