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

Tom 81 / 2008

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


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.


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

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek