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

• Autorzy: Piotr Bogusław Mucha
• Języki publikacji: EN

Abstrakty

EN

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 L₂-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.

Kategorie tematyczne

• 76D05: Navier-Stokes equations
• 35Q30: Navier-Stokes equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 81
• Numer: 1
• Strony: 277-286

Daty

wydano

2008

Twórcy

autor

Piotr Bogusław Mucha

• Institute of Applied Mathematics and Mechanics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/bc81-0-18