Convergence of a Boundary Integral Method for 3-d Water Waves

  title={Convergence of a Boundary Integral Method for 3-d Water Waves},
  author={Thomas Y. Hou and Pingwen Zhang},
We prove convergence of a modified point vortex method for timedependent water waves in a three-dimensional, inviscid, irrotational and incompressible fluid. Our stability analysis has two important ingredients. First we derive a leading order approximation of the singular velocity integral. This leading order approximation captures all the leading order contributions of the original velocity integral to linear stability. Moreover, the leading order approximation can be expressed in terms of… CONTINUE READING