TY - JOUR
T1 - Leray's problem on the stationary Navier-Stokes equations with inhomogeneous boundary data
AU - Kozono, Hideo
AU - Yanagisawa, Taku
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2009
Y1 - 2009
N2 - Consider the stationary Navier-Stokes equations in a bounded domain whose boundary consists of multi-connected components. We investigate the solvability under the general flux condition which implies that the total sum of the flux of the given data on each component of the boundary is equal to zero. Based on our Helmholtz-Weyl decomposition, we prove existence of solutions if the harmonic part of the solenoidal extension of the given boundary data is sufficiently small in L3 compared with the viscosity constant.
AB - Consider the stationary Navier-Stokes equations in a bounded domain whose boundary consists of multi-connected components. We investigate the solvability under the general flux condition which implies that the total sum of the flux of the given data on each component of the boundary is equal to zero. Based on our Helmholtz-Weyl decomposition, we prove existence of solutions if the harmonic part of the solenoidal extension of the given boundary data is sufficiently small in L3 compared with the viscosity constant.
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U2 - 10.1007/s00209-008-0361-2
DO - 10.1007/s00209-008-0361-2
M3 - Article
AN - SCOPUS:77950268740
VL - 262
SP - 27
EP - 39
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 1
ER -