THE CAUCHY PROBLEM FOR SMALL FLUCTUATIONS OF A VISCOUS FLUID IN A WEAK FIELD OF MASS FORCES (O Zadache Koshi dlya Malykh Kolebanii Vyazkoi Zhidkosti v Slabom Ple Massovykh Sil),

Abstract

The paper deals with the Cauchy problem for the unsteady linearized Navier-Stokes equations, representing small deviations of a viscous incompressible fluid from equilibrium in a partially filled motionless vessel in a weak field of force. Surface forces are taken into account, leading to the presence, in the boundary conditions on the surface of the fluid, of a second order differential operator of elliptic type. Existence and uniqueness theorems for the solution of the problem are presented and proved by the methods of functional analysis; an introductory section discusses the decomposition of the Hilbert space L sub 2 (Omega) and derives or gives references to results required later in the paper. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1969
Accession Number
AD0691554

Entities

People

  • N. D. Kopachevskii

Organizations

  • Royal Aircraft Establishment

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Cauchy Problem
  • Decomposition
  • Differential Equations
  • Equations
  • Functional Analysis
  • Hilbert Space
  • Mathematical Analysis
  • Mathematics
  • Navier Stokes Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Information Retrieval

Technology Areas

  • Space