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

• Autorzy: Piotr Bogusław Mucha
• Języki publikacji: EN

Abstrakty

EN

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 $W^{2,1}_r(ℝ³×[k,k+1])$ 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 $W^{2-2/r}_r(ℝ³)$-norm of the perturbing initial data or smallness of the $L_r$-norm of the perturbing force.

Kategorie tematyczne

• 76D05: Navier-Stokes equations
• 35B35: Stability
• 35Q30: Navier-Stokes equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2001
• Tom: 28
• Numer: 3
• Strony: 301-310

Daty

wydano

2001

Twórcy

autor

Piotr Bogusław Mucha

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

Identyfikatory

DOI

10.4064/am28-3-6