Calculus of Variations and Geometric Measure Theory

L. Ambrosio - A. Figalli

On the regularity of the pressure field of Brenier's weak solutions to incompressible Euler equations

created by ambrosio on 14 Jun 2007
modified by figalli on 28 Nov 2008


Accepted Paper

Inserted: 14 jun 2007
Last Updated: 28 nov 2008

Journal: Calc. Var. Partial Differential Equations
Year: 2007


In this paper we improve the regularity in time of the gradient of the pressure field arising in Brenier's variational weak solutions to incompressible Euler equations. This improvement is necessary to obtain that the pressure field is not only a measure, but a function in $L^2_{\rm loc}\left((0,T);BV_{\rm loc}(D)\right)$. In turn, this is a fundamental ingredient in the analysis made in our previous paper of the necessary and sufficient optimality conditions for this variational problem.

Keywords: optimal transportation, Incompressible Euler equations