Annals of Mathematics· 2012Q1
Global solutions for the gravity water waves equation in dimension 3
- 338citations
- Q1SCImago
- 2012year
Short summary
Researchers proved the existence of global solutions for the 3D gravity water waves equation when initial data is small.
AI-generated from the title and abstract; the full text is not read.
Key points
- Global solutions exist for the 3D gravity water waves equation with small data.
- The proof combines energy estimates (controlling L2 norms) with dispersive estimates (ensuring L∞ decay).
- Dispersive estimates are achieved via Fourier space analysis.
- Analysis of space and time resonances is a critical component of the proof.
AI-generated from the title and abstract; the full text is not read.
Abstract
We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of L 2 related norms, with dispersive estimates, which give decay in L . To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.
The authors' abstract, as published at the source. Annals of Mathematics, 2012 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics