# Wydawnictwa / Banach Center Publications / Wszystkie tomy

## Global solutions, structure of initial data and the Navier-Stokes equations

### Tom 81 / 2008

Banach Center Publications 81 (2008), 277-286 MSC: 35Q30, 76D05. DOI: 10.4064/bc81-0-18

#### Streszczenie

In this note we present a proof of existence of global in time regular (unique) solutions to the Navier-Stokes equations in an arbitrary three dimensional domain with a general boundary condition. The only restriction is that the $L_2$-norm of the initial datum is required to be sufficiently small. The magnitude of the rest of the norm is not restricted. Our considerations show the essential role played by the energy bound in proving global in time results for the Navier-Stokes equations.

#### Autorzy

• Piotr Bogus/law MuchaInstitute of Applied Mathematics and Mechanics
Warsaw University
Banacha 2
02-097 Warszawa, Poland
e-mail

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