Accepted Paper

Inserted: 14 jun 2007
Last Updated: 28 nov 2008

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

Abstract:

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

Download:

• pressureSobolev.pdf