Global weak solutions of the 3D compressible semi-geostrophic equations exist for arbitrary compactly supported measure-valued initial data, obtained by semi-discrete optimal transport and particle discretization.
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Semi-discrete optimal transport techniques for the compressible semi-geostrophic equations
Global weak solutions of the 3D compressible semi-geostrophic equations exist for arbitrary compactly supported measure-valued initial data, obtained by semi-discrete optimal transport and particle discretization.