Two dimensional gravity water waves with constant vorticity: I. Cubic lifespan

Abstract

This article is concerned with the incompressible, infinite depth water wave equation in two space dimensions, with gravity and constant vorticity but with no surface tension. We consider this problem expressed in position-velocity potential holomorphic coordinates, and prove local well-posedness for large data, as well as cubic lifespan bounds for small data solutions.

64 pages

Cited by in corpus (7)

• Traveling quasi-periodic water waves with constant vorticity
• Long-time existence for multi-dimensional periodic water waves
• A Lagrangian Interior Regularity Result for the Incompressible Free Boundary Euler Equation with Surface Tension
• A priori estimates for the free-boundary Euler equations with surface tension in three dimensions
• Local Well-posedness for the Motion of a Compressible Gravity Water Wave with Vorticity
• On the Incompressible Limit for the Compressible Free-Boundary Euler Equations with Surface Tension in the Case of a Liquid
• Global Axisymmetric Euler Flows with Rotation