The Large Data of 2D Viscous Surface Waves in Low Regularity

Abstract

We consider the viscous incompressible fluids in a two-dimensional domain bounded below by a fixed smooth boundary and above by a free moving surface. The domain is horizontally periodic or infinite. The fluid dynamics are governed by the Navier–Stokes equations with the effect of gravity and surface tension on the free surface. Here we use a new energy method to develop a sharp local well-posedness theory for the equations with a general free surface in Sobolev spaces for large data.

Keywords

Free boundary problems / Navier–Stokes equations / Surface waves / 35A01 / 35Q30 / 35R35 / 76D05

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Funding

National Natural Science Foundation of China(11901350)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature

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