Global regularity for water waves
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| Title | Global regularity for water waves |
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| Part Number | 8 |
| Number of Parts | 23 |
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| License | You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. |
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| Abstract | We will begin by introducing the water waves equations which are a system of evolution equations modeling the motion of waves (like those in the surface of the ocean), and discuss some of the works done in recent years on the question of long-time regularity.
We will then present a recent result, joint with Deng, Ionescu and Pausader, about global existence of smooth solutions for the 3d gravity-capillary water waves system in infinite depth.
The main difficulties in this problem are the slow decay of linear solutions and the presence of a large set of resonant interactions |
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