On the stability of global solutions to Navier--Stokes equations in the space
The authors consider the global solutions to Navier-Stokes equations in \(\mathbb R^3\) with data being a divergence-free vector-valued distribution. The solutions belong to the space defined by \textit{H. Koch} and \textit{D. Tataru} [Adv. Math. 157, No. 1, 22--35 (2001; Zbl 0972.35084)]. The authors show that the solutions are stable, in the sense that they vanish at infinity (in time), that they depend analytically on their data, and that the set of Cauchy data giving rise to such a solution is open in a specially defined topology. The proof relies on real variable energy estimates which the authors derive from the cancellation property of a trilinear form associated with Navier-Stokes equations.
scientific article; zbMATH DE number 2118448
scientific article