# Estimate of the pressure when its gradient is the divergence of a measure. Applications

ESAIM: Control, Optimisation and Calculus of Variations (2011)

- Volume: 17, Issue: 4, page 1066-1087
- ISSN: 1292-8119

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topBriane, Marc, and Casado-Díaz, Juan. "Estimate of the pressure when its gradient is the divergence of a measure. Applications." ESAIM: Control, Optimisation and Calculus of Variations 17.4 (2011): 1066-1087. <http://eudml.org/doc/272952>.

@article{Briane2011,

abstract = {In this paper, a $W^\{-1,N^\{\prime \}\}$ estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on $\mathbb \{R\}^N$, or on a regular bounded open set of $\mathbb \{R\}^N$. The proof is based partially on the Strauss inequality [Strauss,Partial Differential Equations: Proc. Symp. Pure Math. 23 (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [J. Eur. Math. Soc. 9 (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions which read as the divergence of a measure, and to prove an existence result for the stationary Navier-Stokes equation when the viscosity tensor is only in L1.},

author = {Briane, Marc, Casado-Díaz, Juan},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {pressure; Navier-Stokes equation; div-curl; measure data; fundamental solution},

language = {eng},

number = {4},

pages = {1066-1087},

publisher = {EDP-Sciences},

title = {Estimate of the pressure when its gradient is the divergence of a measure. Applications},

url = {http://eudml.org/doc/272952},

volume = {17},

year = {2011},

}

TY - JOUR

AU - Briane, Marc

AU - Casado-Díaz, Juan

TI - Estimate of the pressure when its gradient is the divergence of a measure. Applications

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2011

PB - EDP-Sciences

VL - 17

IS - 4

SP - 1066

EP - 1087

AB - In this paper, a $W^{-1,N^{\prime }}$ estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on $\mathbb {R}^N$, or on a regular bounded open set of $\mathbb {R}^N$. The proof is based partially on the Strauss inequality [Strauss,Partial Differential Equations: Proc. Symp. Pure Math. 23 (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [J. Eur. Math. Soc. 9 (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions which read as the divergence of a measure, and to prove an existence result for the stationary Navier-Stokes equation when the viscosity tensor is only in L1.

LA - eng

KW - pressure; Navier-Stokes equation; div-curl; measure data; fundamental solution

UR - http://eudml.org/doc/272952

ER -

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