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On the stability of global solutions to Navier–Stokes equations in the space. (English) Zbl 1107.35096

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 H. Koch and 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.

MSC:

35Q30 Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35B35 Stability in context of PDEs

Citations:

Zbl 0972.35084
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