On the regularity of flows with Ladyzhenskaya Shear‐dependent viscosity and slip or non‐slip boundary conditions
On the regularity of flows with Ladyzhenskaya Shear‐dependent viscosity and slip or non‐slip boundary conditions
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DOI：
10.1002/cpa.20036
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发表时间：
2005-04
影响因子：
3
通讯作者：
H. B. Veiga;O. Ladyzhenskaya
中科院分区：
文献类型：
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作者：
H. B. Veiga;O. Ladyzhenskaya
在六十年代，O. A. Ladyzhenskaya和，在梯度依赖粘度的情况下，由J. -L.狮子一个特殊的情况是众所周知的Smagorinsky湍流模型。这是当今研究的一个中心课题。另一方面，在某些情况下，特别是在数值应用中，滑移型边界条件似乎更符合实际。这是一个主要的研究课题。在许多情况下，上述问题在滑移（或非滑移）边界条件下弱解u的存在性是众所周知的。然而，直到边界的规则性仍然提出了许多悬而未决的问题。下面我们给出这类问题在平稳情形下弱解的一些正则性结果，见定理3.1和3.2。演化问题在即将发表的论文[6]中进行了研究;见引言结尾处的注释。© 2004 Wiley Periodicals，Inc.
Navier‐Stokes equations with shear dependent viscosity under the classical non‐slip boundary condition have been introduced and studied, in the sixties, by O. A. Ladyzhenskaya and, in the case of gradient dependent viscosity, by J.‐L. Lions. A particular case is the well known Smagorinsky turbulence model. This is nowadays a central subject of investigation. On the other hand, boundary conditions of slip type seems to be more realistic in some situations, in particular in numerical applications. They are a main research subject. The existence of weak solutions u to the above problems, with slip (or non‐slip) type boundary conditions, is well known in many cases. However, regularity up to the boundary still presents many open questions. In what follows we present some regularity results, in the stationary case, for weak solutions to this kind of problems; see Theorems 3.1 and 3.2. The evolution problem is studied in the forthcoming paper [6]; see the remark at the end of the introduction. © 2004 Wiley Periodicals, Inc.