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

作者:Ifrim Mihaela*; Tataru Daniel
来源:Archive for Rational Mechanics and Analysis, 2017, 225(3): 1279-1346.
DOI:10.1007/s00205-017-1126-z

摘要

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 global solutions.

  • 出版日期2017-9