The Lifespan of Small Data Solutions in Two Dimensional Capillary Water Waves

@inproceedings{Ifrim2014TheLO,
  title={The Lifespan of Small Data Solutions in Two Dimensional Capillary Water Waves},
  author={Mihaela Ifrim and Daniel Tataru},
  year={2014}
}
This article is concerned with the incompressible, irrotational infinite depth water wave equation in two space dimensions, without gravity but with surface tension. We consider this problem expressed in position-velocity potential holomorphic coordinates, and prove that small data solutions have at least cubic lifespan while small localized data leads to… CONTINUE READING