Abstract
For α ∈ (1, 2) we prove that the initial-value problem {∂tu + Dα∂xu + ∂x(u2/2) = 0 on Rx × Rt; u(0) =, is globally well-posed in the space of real-valued L2-functions. We use a frequency dependent renormalization method to control the strong low-high frequency interactions.
Original language | English (US) |
---|---|
Pages (from-to) | 1827-1875 |
Number of pages | 49 |
Journal | Communications in Partial Differential Equations |
Volume | 35 |
Issue number | 10 |
DOIs | |
State | Published - 2010 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Keywords
- Dispersion generalized benjamin-ono equation
- Frequencydependent renormalization
- Global well-posedness
- L initial data