Geodesic
Estimate of the pressure when its gradient is the divergence of a measure. Applications
ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 4, pp. 1066-1087

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In this paper, a W -1,N ' estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on ℝ N , or on a regular bounded open set of 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.

DOI : 10.1051/cocv/2010037
Classification : 35Q30, 35Q35, 35A08
Keywords: pressure, Navier-Stokes equation, div-curl, measure data, fundamental solution 
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     title = {Estimate of the pressure when its gradient is the divergence of a measure. {Applications}},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1066--1087},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {4},
     year = {2011},
     doi = {10.1051/cocv/2010037},
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     zbl = {1232.35113},
     language = {en},
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Briane, Marc; Casado-Díaz, Juan. Estimate of the pressure when its gradient is the divergence of a measure. Applications. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 4, pp. 1066-1087. doi: 10.1051/cocv/2010037

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