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Navier–Stokes equations in aperture domains: Global existence with bounded flux and time-periodic solutions

✍ Scribed by Francesca Crispo; Paolo Maremonti

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 252 KB
Volume: 31
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.903

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✦ Synopsis

Abstract

We consider the Navier–Stokes equations in an aperture domain of the three‐dimensional Euclidean space. We are interested in proving the existence of regular solutions corresponding to small initial data and flux through the aperture. The flux is assumed to be smooth and bounded on (0, +∞). As a consequence, we prove the existence of a time‐periodic solution corresponding to a time‐periodic flux through the aperture. Finally, we compare our solution with a solution belonging to a wider class, showing that, if such a solution does exist, then the two solutions coincide. Copyright © 2007 John Wiley & Sons, Ltd.

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Periodic solutions of the Navier–Stokes equations in a perturbed half-space and an aperture domain

✍ Takayuki Kubo 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 151 KB 👁 1 views

We shall construct a periodic strong solution of the Navier-Stokes equations for some periodic external force in a perturbed half-space and an aperture domain of the dimension n¿3. Our proof is based on L p -L q estimates of the Stokes semigroup. We apply L p -L q estimates to the integral equation