Publications [#246862] of Jian-Guo Liu

Papers Published

1. Duan, Y; Liu, JG, Convergence analysis of the vortex blob method for the b-equation, Discrete and Continuous Dynamical Systems- Series A, vol. 34 no. 5 (May, 2014), pp. 1995-2011, American Institute of Mathematical Sciences (AIMS), ISSN 1078-0947 [doi]
   (last updated on 2025/02/21)

   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.