12 papers
A note on the uniqueness properties of solutions for the Schrödinger-Korteweg de Vries system
Eddye Bustamante, José Jiménez Urrea, Jorge Mejía
In this work we prove that if , , are smooth enough solutions of the coupled Schrödinger-Korteweg-de Vries system \begin{align*} \left. \begin{array}{rl} i u_t+\p…
Dispersive blow-up for a coupled Schrödinger-fifth order KdV system
Eddye Bustamante, José Jiménez Urrea, Jorge Mejía
In this work we establish a dispersive blow-up result for the initial value problem (IVP) for the coupled Schrödinger-fifth order Korteweg-de Vries system \begin{align*} \left. \be…
Dispersive blow-up for the fifth order Korteweg-de Vries equation on the line
Eddye Bustamante, José Jiménez Urrea, Jorge Mejía
In this work we establish a dispersive blow-up result for the initial value problem (IVP) for the fifth order Korteweg-de Vries equation \begin{align*} \left. \begin{array}{rlr} u_…
Local well-posedness and regularity properties for an initial-boundary value problem associated to the fifth order Korteweg-de Vries equation
Eddye Bustamante, José Jiménez Urrea, Jorge Mejía
In this work we prove that the initial-boundary value problem (IBVP) for the fifth order Korteweg-de Vries equation \begin{align*} \left. \begin{array}{rlr} u_t+\partial_x^5 u+u\pa…
On decay and regularity of solutions to the modified 2D Zakharov-Kuznetsov equation
Eddye Alejandro Bustamante, Jose Manuel Jiménez, Alexander Muñoz
This work is devoted to study the relation between regularity and decay for solutions of the two-dimensional modified Zakharov-Kuznetsov equation in the weighted Sobolev spaces $Z_…
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…
The Zakharov-Kuznetsov equation in weighted Sobolev spaces
Eddye Bustamante, José Jiménez, Jorge Mejía
In this work we consider the initial value problem (IVP) associated to the two dimensional Zakharov-Kuznetsov equation $$\left. \begin{array}{rl} u_t+\partial_x^3 u+\partial_x \par…
The Cauchy problem for a fifth order KdV equation in weighted Sobolev spaces
Eddye Bustamante, José Jiménez, Jorge Mejía
In this work we study the initial value problem (IVP) for the fifth order KdV equations, \begin{align*} \partial_{t}u+\partial_{x}^{5}u+u^k\partial_{x}u=0,\text{} & \quad x,t\in \m…
On the support of solutions to the Zakharov-Kuznetsov equation
Eddye Bustamante, Pedro Isaza, Jorge Mejía
In this article we prove that sufficiently smooth solutions of the Zakharov-Kuznetsov equation that have compact support for two different times are identically zero.