Estimate of the pressure when its gradient is the divergence of a measure. Applications
Institut de Recherche Mathématique de Rennes, INSA de Rennes, France. email@example.com
2 Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Spain. firstname.lastname@example.org
Revised: 28 April 2010
In this paper, a estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on , or on a regular bounded open set of . 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.
Mathematics Subject Classification: 35Q30 / 35Q35 / 35A08
Key words: Pressure / Navier-Stokes equation / div-curl / measure data / fundamental solution
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