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

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


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