Abstract
We prove that the KP-I initial-value problem {∂tu + ∂x3u - ∂x -1∂y2u + ∂x(u 2/2) = 0 on ℝx,y2 × ℝt; u(0) = φ, is globally well-posed in the energy space E1(ℝ2) = {φ : ℝ2 → ℝ : ∥φ∥E1(ℝ2) ≈ ∥φ∥L2 + ∥∂xφ∥L2 + ∥∂x -1∂yφ∥L2 < ∞}.
Original language | English (US) |
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Pages (from-to) | 265-304 |
Number of pages | 40 |
Journal | Inventiones Mathematicae |
Volume | 173 |
Issue number | 2 |
DOIs | |
State | Published - Aug 2008 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- General Mathematics