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In connection with the 2-dimensional incompressible Euler equations,Ìýwe study initial data where the vorticityÌýis supported on two wedges, symmetric w.r.t. the origin, with density $O(r^{-\alpha})$.ÌýNumerical simulations by Wen Shen (Oxford, 2017) have shown that, by approximatingÌýthis same initial data with smooth functions in two different ways, one obtainsÌýtwo distinct limit solutions.Ìý One contains a single spiraling vortex,Ìýwhile the other solution contains two vortices.

The talk will report recent work aimed at a rigorous validation of these numerical results.The Ìýmain ingredients are: (i) an analytic construction of the solution in the exterior of a disc,Ìý(ii) Ìýa posteriori error estimates for the numerically computed solution,Ìývalid on a bounded domain where the solution is smooth,Ìýand (iii) Ìýan analytic construction of the solution near the spirals' centers,where singularities occur. This last step is largely based on techniquesÌýintroduced by Volker Elling (2013).