GLOBAL WELL-POSEDNESS FOR THE KLEIN-GORDON EQUATION BELOW THE ENERGY NORM

• 来源期刊: 偏微分方程(英文版)
• 学科: 数学
• 关键词: Klein-Gordon equations Strichartz estimates Besov spaces well-posedness.
• 年，卷（期）: 2004,（2）
• 页码范围: 97-121
• 页数: 25页
• 分类号: O175.27,O175.29.
• 语种: 英文

摘要

We study global well-posedness below the energy norm of the Cauchy problem for the Klein-Gordon equation in Rn with n≥ 3. By means of Bourgain's method along with the endpoint Strichartz estimates of Keel and Tao, we prove the Hs-global well-posedness with s ＜ 1 of the Cauchy problem for the Klein-Gordon equation. This we do by establishing a series of nonlinear a priori estimates in the setting of Besov spaces.