On the Stokes and Navier-Stokes System for Domains with Noncompact Boundary in Lq-spaces
On the Stokes and Navier-Stokes System for Domains with Noncompact Boundary in Lq-spaces
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Lq空间中非紧边界域的Stokes和Navier-Stokes系统
DOI：
10.1002/mana.19941700106
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发表时间：
2006
影响因子：
1
通讯作者：
H. Sohr
中科院分区：
文献类型：
--
作者：
R. Farwig;H. Sohr
我们考虑两类具有非紧边界的无界区域中Stokes和Navier-Stokes方程弱解的Lq-理论，即在扰动半空间IRn中的扰动半空间和在由两个不相交的半空间组成的孔域中的弱解。的证明依赖于切断程序和一个新的乘数方法的半空间问题。在孔域中，我们另外规定通过壁的通量或无穷远处的压降，以选出唯一的解。对于足够小的数据，非线性问题得到了解决，并且需要q =n/2，n ≥ 3，以估计非线性。
We consider the Lq-theory of weak solutions of the Stokes and Navier-Stokes equations in two classes of unbounded domains with noncompact boundary, namely in perturbed half spaces which are obtained by a perturbation of the half space IRn, and in aperture domains consisting of two disjoint half spaces separated by a wall but connected by a hole (aperture) through this wall. The proofs rest on the cut-off procedure and a new multiplier approach to the half space problem. In an aperture domain we additionally prescribe either the flux through the wall or the pressure drop at infinity to single out a unique solution. The nonlinear problem is solved for sufficiently small data and requires q =n/2, n ≥ 3, to estimate the nonlinearity.