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arXiv · 2011.03876

Well-posedness and Regularity for a Polyconvex Energy

Wilfrid Gangbo·Matt Jacobs·Inwon Kim
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Abstract

We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional in two and three dimensions, which corresponds to the $H^1$ 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 construct $L^r$ solutions of the Navier-Stokes equation for a short time interval.

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Wilfrid Gangbo, Matt Jacobs, Inwon Kim. 2020-11-08. Well-posedness and Regularity for a Polyconvex Energy. https://arxiv.org/abs/2011.03876

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