Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Scattering problem for Zakharov-Kuznetsov equation in three space dimensions

Jun-ichi Segata

Abstract

We study the scattering problem for the three dimensional Zakharov-Kuznetsov equation in the framework of the final state problem. We construct a global solution to the Zakharov-Kuznetsov equation which scatters to a given free solution.

Scattering problem for Zakharov-Kuznetsov equation in three space dimensions

Abstract

We study the scattering problem for the three dimensional Zakharov-Kuznetsov equation in the framework of the final state problem. We construct a global solution to the Zakharov-Kuznetsov equation which scatters to a given free solution.
Paper Structure (4 sections, 7 theorems, 96 equations)

This paper contains 4 sections, 7 theorems, 96 equations.

Table of Contents

  1. Introduction
  2. Linear Dispersive Estimates
  3. Bilinear Dispersive Estimates
  4. Proof of Theorem \ref{['main']}

Key Result

Theorem 1.1

Let $0<\delta<1$. Then for any $u_+\in X_{\delta}$, there exists a unique global solution $u\in C(\mathbb{R}; H^1(\mathbb{R}^2))$ to (ZK) satisfying for any $t\ge1$, where $\alpha>1/2$. Similar result holds for negative time direction.

Theorems & Definitions (17)

  • Theorem 1.1
  • Remark 1
  • Remark 2
  • Remark 3
  • Lemma 2.1
  • proof : Proof of Lemma \ref{['lemL']}.
  • Proposition 3.1
  • Lemma 3.2
  • proof : Proof of Lemma \ref{['algebra']}.
  • proof : Proof of Proposition \ref{['xF']}.
  • ...and 7 more