A Study of Weak Solutions and their Regularizations by Numerical Methods

Abstract

Consider the incompressible Euler equations with vortex sheet initial data. For this initial value problem, there are a number of outstanding conjectures: This initial value problem does not have a unique weak or measure- valued solution, a selection principle is required to pick out a unique solution. The limit of vanishing viscosity (in the Navier Stokes equations) provides the correct selection principle, and different regularizations, such as adding viscosity or smoothing the initial vortex sheet, may converge to different limits as the regularization tends to zero.

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Document Details

Document Type
Technical Report
Publication Date
Jun 30, 1993
Accession Number
ADA277453

Entities

People

  • George Majda

Organizations

  • Ohio State University

Tags

DTIC Thesaurus Topics

  • Air Force
  • Analogs
  • Applied Mathematics
  • Boltzmann Equation
  • Computations
  • Electric Fields
  • Electron Density
  • Electrons
  • Equations
  • Euler Equations
  • High Resolution
  • Mathematical Analysis
  • Mathematics
  • Navier Stokes Equations
  • Poisson Equation
  • Stratified Fluids
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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