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By George Elmer Forsythe, Michael A. Malcolm, Cleve B. Moler

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Univ. Padova, 31:308-340. , Meyer, Y. and Semmes, S. (1993). Compensated compactness and Hardy spaces. J. Math. , 72(3):247-286. P. (1994). An introduction to the mathematical theory of the NavierStokes equations, volume II. Springer tracts in natural philosophy. [9] Girault, V. and Sequeira, A. (1991). A well posed problem for the exterior Stokes equations in two and three dimensions. Arch. Rational Mech. , 114:313-333. [10] Girault, V. A. (1986). Finite Element Approximation of the Navier-Stokes Equations.

2. 3 that we can associate with each weak solution u a pressure that locally belongs to But, we do not have yet any information concerning the integrability at infinity of Our first result is dedicated to this question. 3. 3 has a representative such that with Proof. 3 and let be the associated pressure. 1. 2 yields besides that so we get that and ii) We consider now the other terms of Since is bounded and has bounded derivatives with compact support, it is easy to check that the terms and belong to Proving that is even simpler.

Indiana Univ. Math. , 40:1-25. [12] Kozono, H. and Sohr, H. (1992). On a new class of generalized solutions for the Stokes equations in exterior domains. Ann. Scuola Norm. Sup. Pisa, Ser. IV, 19:155-181. [13] Leray, J. (1934). Sur le mouvement d’un liquide visqueux emplissant l’espace. , 63:193-248. [14] Nirenberg, L. (1959). On elliptic partial differential equations. Ann. Scuola Norm. Sup. Pisa, 13:116-162. [15] Specovius Neugebauer, M. (1994). Weak Solutions of the Stokes Problem in Weighted Sobolev Spaces.

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