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SIAM J. on Numerical Analysis / Volume 50 / Issue 1

SIAM J. Numer. Anal. 50, pp. 1-21 (21 pages)

Convergence of a Particle Method and Global Weak Solutions of a Family of Evolutionary PDEs

Alina Chertock, Jian-Guo Liu, and Terrance Pendleton

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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

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KEYWORDS

AMS Subject Headings

35B65, 35C08, 35D05, 35L65, 37K10, 65M25, 74J35, 76B15

PUBLICATION DATA

ISSN

0036-1429 (print)  
1095-7170 (online)

Publisher

$abstract.society.value is a Member of CrossRef Society for Industrial and Applied Mathematics

ARTICLE DATA

History
Received April 18, 2011
Accepted September 22, 2011
Published online January 19, 2012
Digital Object Identifier
http://dx.doi.org/10.1137/110831386

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