Small-time existence for the three-dimensional Navier-Stokes equations for an incompressible fluid with a free surface
type: Item
instance of: scholarly article
title: Small-time existence for the three-dimensional Navier-Stokes equations for an incompressible fluid with a free surface
zbMATH Open document ID: 0857.76026
DOI: 10.1007/BF00375146
author: Atusi Tani
published in: Archive for Rational Mechanics and Analysis
publication date: 1997-03-17T00:00:00Z
review text: The author proves the local existence theorem for incompressible fluid flow under the condition that both the fixed bottom and free surface of fluid tend to constants at infinity. The study uses the complicated technique of Sobolev-Slobodeskij spaces and is based on the decomposition of the solution into the sum of solutions of a linear system and a nonlinear perturbation. Global existence theorem for the linear system uses actively Solonnikov's results, whereas the local existence theorem for the nonlinear perturbation problem is proved by the method of successive approximations.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 911920
zbMATH Keywords: decomposition of solution
zbMATH Keywords: local existence theorem
zbMATH Keywords: Sobolev-Slobodeskij spaces
zbMATH Keywords: linear system
zbMATH Keywords: nonlinear perturbation
zbMATH Keywords: method of successive approximations
reviewed by: P. B. Dubovski
MaRDI profile type: Publication
cites work: Small-time existence for the Navier-Stokes equations with a free surface
cites work: The initial value problem for the navier-stokes equations with a free surface
cites work: Large-time regularity of viscous surface waves
cites work: Q3783708
cites work: Q5576913
cites work: Equations of fluid dynamics—free surface problems
cites work: Q4115553
cites work: Q4133311
cites work: Q4118226
cites work: SOLVABILITY OF A PROBLEM ON THE MOTION OF A VISCOUS INCOMPRESSIBLE FLUID BOUNDED BY A FREE SURFACE
cites work: Q3343626
cites work: Q4721792
cites work: Q3770169
cites work: Q3199084
cites work: Large time existence of small viscous surface waves without surface tension
cites work: Q4700617
cites work: Q4321140
cites work: Large-time existence of surface waves in incompressible viscous fluids with or without surface tension
cites work: The initial value problem for viscous incompressible flow down an inclined plane
cites work: On the Navier-Stokes flow down an inclined plane
description: scientific article; zbMATH DE number 911920