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On the radius of spatial analyticity for the Majda-Biello and Hirota-Satsuma systems

Seongyeon Kim, Ihyeok Seo

Abstract

We investigate the persistence of spatial analyticity for solutions to the Majda-Biello and Hirota-Satsuma systems with analytic initial data. This result is the first to establish analyticity persistence in such coupled KdV systems.

On the radius of spatial analyticity for the Majda-Biello and Hirota-Satsuma systems

Abstract

We investigate the persistence of spatial analyticity for solutions to the Majda-Biello and Hirota-Satsuma systems with analytic initial data. This result is the first to establish analyticity persistence in such coupled KdV systems.

Paper Structure

This paper contains 9 sections, 9 theorems, 82 equations, 2 tables.

Table of Contents

  1. Introduction
  2. Function spaces
  3. Bilinear estimates in Gevrey-Bourgain spaces
  4. Local well-posedness and almost conservation law
  5. Local well-posedness
  6. Almost conservation law
  7. Proof of Theorem \ref{['thm1']}
  8. The case $s=0$
  9. The general case $s \in \mathbb{R}$

Key Result

Theorem 1.1

Let $u,v$ be the global solution of ssys with $(u_0,v_0)\in\mathcal{G}^{\sigma_0,s}(\mathbb R)$ for some $\sigma_0>0$ and $s\in\mathbb R$. If the coefficients $c_{ij}$$(i,j=1,2)$ fall into any of the cases vary depending on the value of $a_2/a_1$ as in Table table3, then for all $t\in\mathbb R$ with $\sigma(t)\ge c|t|^{-4/3-\epsilon}$ for any $\epsilon>0$ as $|t|\rightarrow\infty$. Here, $c>0$ is

Theorems & Definitions (12)

  • Theorem 1.1
  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Lemma 3.1
  • Lemma 3.2
  • proof
  • Theorem 4.1
  • proof
  • Lemma 4.2
  • ...and 2 more