## Stability estimate for strong solutions of the Navier-Stokes system and its applications

### Summary

Summary: We obtain a `stability estimate' for strong solutions of the Navier-Stokes system, which is an $L^\alpha$-version, $1 less than \alpha less than \infty$, 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.

35Q30, 76D05

### Keywords/Phrases

Navier-Stokes system, strong solutions, stability, uniqueness, non-blowup condition