On the Solvability of the Stokes and Navier-Stokes Problems in the Domains That Are Layer-Like at Infinity
On the Solvability of the Stokes and Navier-Stokes Problems in the Domains That Are Layer-Like at Infinity
复制标题
无穷远层状域中斯托克斯和纳维-斯托克斯问题的可解性
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
K. Pileckas
中科院分区：
文献类型：
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作者：
S. Nazarov;K. Pileckas
证明了在球外与三维层ℝ2×(0，1)重合的区域中，存在Stokes问题和N-S问题的弱解。除了具有有限Dirichlet积分的解之外，线性问题的解被构造成在无穷远处具有规定的行为，使得平面平行的Poiseuille流和Couette流，旋转流。在数据小的假设下，找到了一个非线性问题的解，它将一个非零流驱动到无穷大，并且变得唯一。给出了压力的加权范数的估计。
Weak solutions to the Stokes and Navier-Stokes problems are proved to exist in domains which, outside a ball, coincide with the three-dimensional layer ℝ2 × (0,1). Apart from solutions with the finite Dirichlet integral, solutions to the linear problem are constructed with a prescribed behavior at infinity such that the plane-parallel Poiseuille and Couette flows, the rotational flow. A solution to the nonlinear problem is found that drives a nonzero flux to infinity and becomes unique under the data smallness assumption. Estimates for weighted norms of the pressure are derived as well