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  1. Free, publicly-accessible full text available September 1, 2025
  2. We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional in two and three dimensions, which corresponds to theH1-projection of measure-preserving maps. Our result introduces a new criteria on the uniqueness of the minimizer, based on the smallness of the lagrange multiplier. No estimate on the second derivatives of the pressure is needed to get a unique global minimizer. As an application, we construct a minimizing movement scheme to constructLr-solutions of the Navier–Stokes equation (NSE) for a short time interval. 
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