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We initiate the study of M-strings in the thermodynamic limit. In this limit the BPS partition function of M5 branes localizes on configurations with a large number of strings which leads to a reformulation of the partition function in terms of a matrix model. We solve this matrix model and obtain its spectral curve which can be interpreted as the Seiberg-Witten curve associated to the compactified M5 brane theory.

We prove the convergence of a discontinuous Galerkin method approximating the 2-D incompressible Euler equations with discontinuous initial vorticity:$omega_0 in L^2(Omega)$. Furthermore, when $omega_0 in L^infty(Omega)$, the whole sequence is shown to be strongly convergent. This is the first convergence result in numerical approximations of this general class of discontinuous flows. Some important flows such as vortex patches belong to this class.