@article{chertock_liu_pendleton_2012, title={CONVERGENCE OF A PARTICLE METHOD AND GLOBAL WEAK SOLUTIONS OF A FAMILY OF EVOLUTIONARY PDES}, volume={50}, ISSN={["1095-7170"]}, url={https://doi-org.prox.lib.ncsu.edu/10.1137/110831386}, DOI={10.1137/110831386}, abstractNote={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.}, number={1}, journal={SIAM JOURNAL ON NUMERICAL ANALYSIS}, author={Chertock, Alina and Liu, Jian-Guo and Pendleton, Terrance}, year={2012}, pages={1–21} }