Convergence of a particle method and global weak solutions of a family of evolutionary PDEs

Published

Journal Article

The purpose of this paper is to provide global existence and uniqueness results for a family of fluid transport equations by establishing convergence results for the particle method applied to these equations. The considered family of PDEs is a collection of strongly nonlinear equations which yield traveling wave solutions and can be used to model a variety of flows in fluid dynamics. We apply a particle method to the studied evolutionary equations and provide a new self-contained method for proving its convergence. The latter is accomplished by using the concept of space-time bounded variation and the associated compactness properties. From this result, we prove the existence of a unique global weak solution in some special cases and obtain stronger regularity properties of the solution than previously established. © 2012 Society for Industrial and Applied Mathematics.

Full Text

Duke Authors

Cited Authors

  • Chertock, A; Liu, JG; Pendleton, T

Published Date

  • May 28, 2012

Published In

Volume / Issue

  • 50 / 1

Start / End Page

  • 1 - 21

International Standard Serial Number (ISSN)

  • 0036-1429

Digital Object Identifier (DOI)

  • 10.1137/110831386

Citation Source

  • Scopus