Stability of Constant Solutions to the Navier–Stokes System in ${\Bbb R}^3$

Volume 28 / 2001

Piotr Bogus/law Mucha Applicationes Mathematicae 28 (2001), 301-310 MSC: 35B35, 35Q30, 76D05. DOI: 10.4064/am28-3-6


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 $W^{2,1}_r({\Bbb R}^3\times [k,k+1])$ for $k\in {\Bbb N}$. The result is obtained under the assumption of smallness of the $L_2$-norm of the perturbing initial data. We do not assume smallness of the $W^{2-2/r}_r({\Bbb R}^3)$-norm of the perturbing initial data or smallness of the $L_r$-norm of the perturbing force.


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

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