Global well-posedness of the KP-I initial-value problem in the energy space

• 成果类型: Article
• 署名作者: Ionescu, A. D.; Kenig, C. E.; Tataru, D.
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; University of Chicago; University of California System; University of California Berkeley
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-008-0115-0
• 发表日期: 2008
• 页码: 265-304
• 关键词: korteweg-devries equation; solitary waves; asymptotic stability; instability; EXISTENCE; solitons

摘要

We prove that the KP-I initial-value problem {partial derivative(t)u + partial derivative(3)(x)u - partial derivative(-1)(x)partial derivative(2)(y)u + partial derivative(x)(u(2)/2) = 0 on R-x,y(2) x R-t; u(0) =phi is globally well-posed in the energy space E-1(R-2) = {phi : R-2 -> R : parallel to phi parallel to(E1(R2)) approximate to parallel to phi parallel to(L2) + parallel to partial derivative(x)phi parallel to(L2) + parallel to partial derivative(-1)(x)partial derivative(y)phi parallel to(L2) < infinity}.