Global Well-Posedness for Dissipative Korteweg-de Vries Equations

被引：10

作者：

Vento, Stephane ^{[1
]}

机构：

[1] Univ Paris Est, Lab Anal & Math Appl, F-77454 Champs Sur Marne 2, Marne La Vallee, France

来源：

FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA | 2011年 / 54卷 / 01期

关键词：

KdV-like equations; Bourgain spaces; Cauchy problem; CAUCHY-PROBLEM; BURGERS-EQUATION; SOBOLEV SPACES; KDV EQUATION;

D O I：

10.1619/fesi.54.119

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to the well-posedness for dissipative KdV equations u(t) + u(xxx) + vertical bar D-x vertical bar(2 alpha)u + uu(x) = 0, 0 < alpha <= 1. An optimal bilinear estimate is obtained in Bourgain's type spaces, which provides global well-posedness in H-s(R), s > -3/4 for alpha <= 1/2 and s > -3/(5 - 2 alpha) for alpha > 1/2.

引用

页码：119 / 138

页数：20

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