Leray's problem on the stationary Navier-Stokes equations with inhomogeneous boundary data

Hideo Kozono; Taku Yanagisawa

doi:10.1007/s00209-008-0361-2

Leray's problem on the stationary Navier-Stokes equations with inhomogeneous boundary data

Hideo Kozono^*, Taku Yanagisawa

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

44 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	27-39
Number of pages	13
Journal	Mathematische Zeitschrift
Volume	262
Issue number	1
DOIs	https://doi.org/10.1007/s00209-008-0361-2
Publication status	Published - 2009
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00209-008-0361-2

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abstract = "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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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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Leray's problem on the stationary Navier-Stokes equations with inhomogeneous boundary data

Abstract

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