Pedro Isaza

LOCAL AND GLOBAL CAUCHY PROBLEMS FOR THE KADOMTSEV–PETVIASHVILI (KP–II) EQUATION IN SOBOLEV SPACES OF NEGATIVE INDICES

It is proved that the Cauchy problem for the Kadomtsev-Petviashvili II (KPII) equation is locally well posed in the anisotropic Sobolev spaces H s 1 s 2 (R 2) with s 1 > −⅓ and s 2 ≥ 0, and globally well posed in H s 10(R 2) with s 1 > − . This article is partially supported by Colciencias, Colombia, grant: 1118-05-605-96.

On Decay Properties of Solutions of the k-Generalized KdV Equation

We prove special decay properties of solutions to the initial value problem associated to the k-generalized Korteweg-de Vries equation. These are related with persistence properties of the solution flow in weighted Sobolev spaces and with sharp unique continuation properties of solutions to this equation. As an application of our method we also obtain results concerning the decay behavior of perturbations of the traveling wave solutions as well as results for solutions corresponding to special data.

On the Propagation of Regularity and Decay of Solutions to the k-Generalized Korteweg-de Vries Equation

We study special regularity and decay properties of solutions to the IVP associated to the k-generalized KdV equations. In particular, for datum u 0 ∈ H 3/4+ (ℝ) whose restriction belongs to H l ((b, ∞)) for some l ∈ ℤ+ and b ∈ ℝ we prove that the restriction of the corresponding solution u(·, t) belongs to H l ((β, ∞)) for any β ∈ ℝ and any t ∈ (0, T). Thus, this type of regularity propagates with infinite speed to its left as time evolves.

On the Propagation of Regularity of Solutions of the Kadomtsev--Petviashvili Equation

We shall deduce some special regularity properties of solutions to the IVP associated to the Kadomtsev--Petviashvili equation. Mainly, for datum

Global Cauchy problem for the Ostrovsky equation

u_0\in X_s(\mathbb{R}^2)

Cauchy problem for the Ostrovsky equation in spaces of low regularity

,

Cauchy problem for the fifth order Kadomtsev-Petviashvili (KPII) equation

s>2

On the support of solutions to the Zakharov–Kuznetsov equation

(see (1.2) below) whose restriction belongs to

On the support of solutions to the Ostrovsky equation with negative dispersion

H^m((x_0,\infty)\times\mathbb{R})

Unique continuation principle for the Ostrovsky equation with negative dispersion

for some