Riv. Mat. Univ. Parma, Vol. 1, No. 1, 2010


Solutions of the Navier-Stokes equations constructed by artificial compressibility approximation are suitable

Pages: 219-230
Received: 28 January 2010   
Accepted: 25 March 2010
Mathematics Subject Classification (2000): 35Q10, 76N10, 76D05.

Keywords: Navier-Stokes equations, suitable weak solutions.

Abstract: In this paper we prove that weak solution constructed by artificial compressibility method are suitable in the sense of Scheffer, [18], [19]. Using Hilbertian setting and Fourier transform with respect to the time we obtain nontrivial estimates of the pressure and the time derivate of the velocity field which allow us to pass into the limit.

[18] V. Scheffer, Partial regularity of solutions to the Navier-Stokes equations, Pacific J. Math. 66 (1976), 535-552.
[19] V. Scheffer, Hausdorff measure and the Navier-Stokes equations, Comm. Math. Phys. 55 (1977), 97-112.

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