| Issue |
ESAIM: COCV
Volume 29, 2023
|
|
|---|---|---|
| Article Number | 67 | |
| Number of page(s) | 40 | |
| DOI | https://doi.org/10.1051/cocv/2023041 | |
| Published online | 11 August 2023 | |
Well-posedness and regularity for a polyconvex energy
1
Department of Mathematics, UCSB, Isla Vista CA, 93117 USA
2
Purdue University, IN 47907, USA
* Corresponding author: majaco@ucsb.edu
Received:
13
October
2022
Accepted:
16
May
2023
We prove the existence, uniqueness, and regularity of minimizers of a polyconvex functional in two and three dimensions, which corresponds to the H1-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 Lr-solutions of the Navier–Stokes equation (NSE) for a short time interval.
Mathematics Subject Classification: 49K20 / 49K35 / 49N15 / 76D05
Key words: Calculus of variations / polyconvexity / convex duality / Ekeland variational principle / Navier-Stokes
© The authors. Published by EDP Sciences, SMAI 2023
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