Global solutions for the gravity water waves system in 2d

By A. Ionescu, F. Pusateri. Inventiones Mathematicae, 2013

241 citations recorded by the source corpus.

We consider the gravity water waves system in the case of a one dimensional interface, for sufficiently smooth and localized initial data, and prove global existence of small solutions. This improves the almost global existence result of Wu (Invent Math 177(1):45–135, 2009). We also prove that the asymptotic behavior of solutions as time goes to infinity is different from linear, unlike the three dimensional case (Germain et al., Ann Math 175(2):691–754, 2012; Wu, Invent Math 184(1):125–220, 2011). In particular, we identify a suitable nonlinear logarithmic correction and show modified scattering. The solutions we construct in this paper appear to be the first global smooth nontrivial solutions of the gravity water waves system in 2D.

Subfields: Applied Mathematics, Mathematical Physics, Oceanography

View Paper: https://www.semanticscholar.org/paper/9b6d25b336ccc54671fc25e8e7968408ae4c3822

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Riccardo Montalto
2. Pierre Baldi
3. E. Haus
4. Massimiliano Berti
5. Jean-Marc Delort
6. Thomas Alazard

In Mathematical Physics

1. Riccardo Montalto
2. Massimiliano Berti
3. Pierre Baldi
4. E. Haus
5. Jean-Marc Delort
6. Thomas Alazard
7. Michela Procesi
8. Dario Bambusi

In Oceanography

1. Jean-Marc Delort
2. Massimiliano Berti
3. Riccardo Montalto
4. Pierre Baldi
5. Thomas Alazard
6. E. Haus

Citations in the corpus

• Asymptotic stability of solitons for mKdV (2015, unknown): “A similar approach was also successfully employed in the proofs of global regularity and modified scattering for 2d gravity [23, 24, 25] and capillary [26, 27] water waves, and in other higher dimensional dispersive models [29, 49].”
• Time quasi-periodic gravity water waves in finite depth (2017, methodology): “d = 1) it has been proved by Alazard-Delort [4] and Ionescu-Pusateri [36].”
• Global solutions and asymptotic behavior for two dimensional gravity water waves (2013, background): “An important question is to determine whether the lifespan could be finite.”