Publications [#246893] of Jian-Guo Liu

Papers Published

1. Chertock, A; Liu, JG; Pendleton, T, Convergence of a particle method and global weak solutions of a family of evolutionary PDEs, SIAM J. Numer. Anal., vol. 50 no. 1 (2012), pp. 1-21, Society for Industrial & Applied Mathematics (SIAM), ISSN 0036-1429
   (last updated on 2024/04/19)

   Abstract:
   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.