Nonlinear Partial Differential Equations Using Compactness.

Abstract

After reviewing some general properties of Sobolev's spaces the author gives an abstract framework for Navier-Stokes equations. He examines some technical properties of the functional spaces introduced and proves existence of a solution: this is done using Galerkin's method and a compactness theorem for the limiting procedure. Uniqueness and regularity properties are proved in dimension 2. Bounded, periodic and stationary solutions are studied as well as stability of small periodic or stationary solutions. The same method is applied to 2 semilinear wave equations. This is done after studying the invariants of the wave equation with application to local decay of energy.

Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1976
Accession Number
ADA028230

Entities

People

  • L. Tartar

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Differential Equations
  • Equations
  • Mathematical Analysis
  • Navier Stokes Equations
  • Partial Differential Equations
  • Stationary
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis

Technology Areas

  • Space