Leray’s problem on the stationary Navier–Stokes equations with inhomogeneous boundary data
Leray’s problem on the stationary Navier–Stokes equations with inhomogeneous boundary data
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DOI：
10.1007/s00209-008-0361-2
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发表时间：
2009
影响因子：
0.8
通讯作者：
H. Kozono;T. Yanagisawa
中科院分区：
文献类型：
--
作者：
H. Kozono;T. Yanagisawa
考虑有界区域中定常的Navier-Stokes方程，其边界由多连通分量组成。我们研究了在一般通量条件下的可解性，即给定数据在边界各分量上的通量之和等于零。基于我们的Helmholtz-Weyl分解，我们证明了当给定边界数据的螺线延拓的调和部分在L3中与粘性常数相比足够小时，解的存在性。
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 inL3compared with the viscosity constant.