TY - JOUR

T1 - Uniform estimates in the velocity at infinity for stationary solutions to the Navier-Stokes exterior problem

AU - Shibata, Yoshihiro

AU - Yamazaki, Masao

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2005

Y1 - 2005

N2 - This paper is concerned with the stationary Navier-Stokes equations in exterior domains of dimension n ≥ 3, and provides a sufficient condition on the external force for the unique solvability. This condition is valid both in the case with small but nonzero velocity at infinity, and in the case with zero velocity at infinity. As a result it is proved that, if the external force satisfies this condition, the solution with nonzero velocity at infinity converges to the solution with zero velocity at infinity with respect to the weak-∗ topology of appropriate function spaces.

AB - This paper is concerned with the stationary Navier-Stokes equations in exterior domains of dimension n ≥ 3, and provides a sufficient condition on the external force for the unique solvability. This condition is valid both in the case with small but nonzero velocity at infinity, and in the case with zero velocity at infinity. As a result it is proved that, if the external force satisfies this condition, the solution with nonzero velocity at infinity converges to the solution with zero velocity at infinity with respect to the weak-∗ topology of appropriate function spaces.

KW - Lorentz spaces

KW - Navier-Stokes equation

KW - Oseen equation

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U2 - 10.4099/math1924.31.225

DO - 10.4099/math1924.31.225

M3 - Article

AN - SCOPUS:33744524308

SN - 0289-2316

VL - 31

SP - 225

EP - 279

JO - Japanese Journal of Mathematics

JF - Japanese Journal of Mathematics

IS - 2

ER -