Abstract
AbstractWe study a fundamental model in fluid mechanics—the 3D gravity water wave equation, in which an incompressible fluid occupying half the 3D space flows under its own gravity. In this paper we show long‐term regularity of solutions whose initial data is small but not localized.Our results include: almost global well‐posedness for unweighted Sobolev initial data and global well‐posedness for weighted Sobolev initial data with weight |x|α for any α > 0. In the periodic case, if the initial data lives on an R by R torus, and ϵ close to the constant solution, then the life span of the solution is at least R/ϵ2(logR)2. © 2021 Wiley Periodicals LLC.
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