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A note on the generic solvability of the Navier-Stokes equations. (English) Zbl 0712.35078

The author considers the Navier-Stokes equations in a three-dimensional bounded domain. For any fixed initial velocity, H. Sohr and W. von Wahl [Hiroshima Math. J. 17, 613-625 (1987; Zbl 0676.35073)] have proved a density property for the set of external forces for which global solutions exist. In the present paper the same result is proved by means of a simpler approach.
Reviewer: P.Secchi

MSC:

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids

Citations:

Zbl 0676.35073
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References:

[1] H. Beirão Da Veiga , On the construction of suitable weak solutions to the Navier-Stokes equations via a general approximation theorem , J. Math. Pures Appl. , 64 ( 1985 ), pp. 321 - 334 . MR 823407 | Zbl 0615.35068 · Zbl 0615.35068
[2] A.V. Fursikov , On some problems of control and results concerning the unique solvability of a mixed boundary value problem for the three-dimensional Navier-Stokes and Euler systems , Dokl. Akad. Nauk SSSR , 252 ( 1980 ), pp. 1066 - 1070 . MR 576448 | Zbl 0481.35001 · Zbl 0481.35001
[3] H. Sohr - W. VON WAHL, Generic solvability of the equations of Navier-Stokes , Hiroshima Math. J. , 17 ( 1987 ), pp. 613 - 625 . MR 920717 | Zbl 0676.35073 · Zbl 0676.35073
[4] V.A. Solonnikov , Estimates for the solutions of nonstationary Navier-Stokes equations , J. Soviet Math. , 8 ( 1977 ), pp. 467 - 529 . Zbl 0404.35081 · Zbl 0404.35081
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