ON THE NAVIER-STOKES INITIAL VALUE PROBLEM, I,

Abstract

The initial value problem for the nonstationary Navier-Stokes equation is considered. New results were obtained with the aid of various methods from modern functional analysis. The existence of unique and global (in time) solutions for 2-dimensional flows as well as the existence of unique and local (in time) solutions for 3-dimensional flows was established. In most of these works the word solution was interpreted in a generalized sense. The purpose is to deduce such existence theorems for 3-dimensional flows through a Hilbert space approach, making use of the theory of fractional powers of operators and the theory of semi-groups of operators. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 11, 1963
Accession Number
AD0422336

Entities

People

  • Hiroshi Fujita
  • Tosio Kato

Organizations

  • Stanford University

Tags

DTIC Thesaurus Topics

  • Equations
  • Functional Analysis
  • Hilbert Space
  • Mathematical Analysis
  • Mathematics
  • Navier Stokes Equations
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space