Vol. 104, No. 1, 1983

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On the best conditions on the gradient of pressure for uniqueness of viscous flows in the whole space

Giovanni P. Galdi and Salvatore Rionero

Vol. 104 (1983), No. 1, 77–83

In this paper we prove a uniqueness theorem for the Cauchy problem of the Navier-Stokes equations under the assumption on the gradient of pressure p that it either belongs to some Lq space for some q (1,) or tends to zero at large spatial distances. As shown by means of a counterexample, in the class where uniqueness is proven the above hypotheses cannot be relaxed to p only bounded.

Mathematical Subject Classification 2000
Primary: 35Q10, 35Q10
Secondary: 76D05
Received: 9 July 1980
Published: 1 January 1983
Giovanni P. Galdi
Salvatore Rionero