Convergence analysis of the vortex blob method for the $b$-equation

Yong Duan; Jian-Guo Liu

doi:10.3934/dcds.2014.34.1995

Article Contents

2014, Volume 34, Issue 5: 1995-2011. Doi: 10.3934/dcds.2014.34.1995

This issue Previous Article Multi-existence of multi-solitons for the supercritical nonlinear Schrödinger equation in one dimension Next Article Analytic skew-products of quadratic polynomials over Misiurewicz-Thurston maps

Convergence analysis of the vortex blob method for the $b$-equation

Yong Duan^1, and
Jian-Guo Liu^2,

1.
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan, 611731
2.
Department of Physics and Department of Mathematics, Duke University, Durham, NC 27708

Received: February 2013

Revised: July 2013

Published: May 2014

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we prove the convergence of the vortex blob method for a family of nonlinear evolutionary partial differential equations (PDEs), the so-called b-equation. This kind of PDEs, including the Camassa-Holm equation and the Degasperis-Procesi equation, has many applications in diverse scientific fields. Our convergence analysis also provides a proof for the existence of the global weak solution to the b-equation when the initial data is a nonnegative Radon measure with compact support.

Keywords:

Mathematics Subject Classification: Primary: 35B65, 35C08, 35D30, 37K10, 65M75, 76B15; Secondary: 35Q51.

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