Stability of Constant Solutions to the Navier-Stokes System in ℝ³

Piotr Bogusław Mucha

Applicationes Mathematicae, Tome 28 (2001), p. 301-310 / Harvested from The Polish Digital Mathematics Library

Résumé

The paper examines the initial value problem for the Navier-Stokes system of viscous incompressible fluids in the three-dimensional space. We prove stability of regular solutions which tend to constant flows sufficiently fast. We show that a perturbation of a regular solution is bounded in $W_{r}^{2, 1} (ℝ ³ \times [k, k + 1])$ for k ∈ ℕ. The result is obtained under the assumption of smallness of the L₂-norm of the perturbing initial data. We do not assume smallness of the $W_{r}^{2 - 2 / r} (ℝ ³)$ -norm of the perturbing initial data or smallness of the $L_{r}$ -norm of the perturbing force.

Publié le : 2001-01-01

Zbl 1009.35060

EUDML-ID : urn:eudml:doc:279036

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     year = {2001},
     pages = {301-310},
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Piotr Bogusław Mucha. Stability of Constant Solutions to the Navier-Stokes System in ℝ³. Applicationes Mathematicae, Tome 28 (2001) pp. 301-310. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-3-6/