Yuuki Shimizu

Continuation and reduction of steady vortex sheets under metric deformations on a disk

We study the local continuation of a steady vortex sheet under a prescribed deformation $g_s= e^{2\sigma_s}g_{\mathrm{e}}$ of a conformal metric on the unit disk. Representing the moving sheet by a normal graph, we formulate the streamline and Bernoulli conditions as a nonlinear residual whose two components have diffe...