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

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 N , or on a regular bounded open set of  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 : https://doi.org/10.1051/cocv/2010037
Classification:  35Q30,  35Q35,  35A08
Keywords: pressure, Navier-Stokes equation, div-curl, measure data, fundamental solution
@article{COCV_2011__17_4_1066_0,
     author = {Briane, Marc and Casado-D\'\i az, Juan},
     title = {Estimate of the pressure when its gradient is the divergence of a measure. Applications},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {4},
     year = {2011},
     pages = {1066-1087},
     doi = {10.1051/cocv/2010037},
     zbl = {1232.35113},
     mrnumber = {2859865},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2011__17_4_1066_0}
}
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, Volume 17 (2011) no. 4, pp. 1066-1087. doi : 10.1051/cocv/2010037. http://www.numdam.org/item/COCV_2011__17_4_1066_0/

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