We obtain a `stability estimate' for strong solutions of the Navier-Stokes system, which is an -version, , of the estimate that Serrin [Se] used in obtaining uniqueness of weak solutions to the Navier-Stokes system. By applying this estimate, we obtain new results in stability and uniqueness of solutions, and non-blowup conditions for strong solutions.
Submitted February 17, 1998. Published June 3, 1998.
Math Subject Classification: 35Q30, 76D05.
Key Words: Navier-Stokes system, strong solutions, stability, uniqueness, non-blowup condition.
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Department of Applied Mathematics
Faculty of Engineering, Shizuoka University
Hamamatsu 432, Japan