Convergence analysis of the vortex blob method for the $b$-equation
Convergence analysis of the vortex blob method for the $b$-equation
In this paper, we prove the convergence of the vortex blob method for a family ofnonlinear 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 …