Global Solvability in W22,1-Weighted Spaces of the Two-Dimensional Navier–Stokes Problem in Domains with Strip-Like Outlets to Infinity
Global Solvability in W22,1-Weighted Spaces of the Two-Dimensional Navier–Stokes Problem in Domains with Strip-Like Outlets to Infinity
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具有无穷大带状出口域中二维纳维-斯托克斯问题在 W22,1 加权空间中的全局可解性
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发表时间：
2008
期刊：
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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：
K. Pileckas
摘要：在加权Sobolev函数空间中，研究了二维区域中的含时Navier-Stokes方程组。证明了在自然相容条件下，存在一个唯一的解，该解在出口截面上的通量为无穷大，且在每个出口处趋向于相应的时变Poiffille流。所获得的结果对于数据的任意大范数（特别是对于任意通量）和时间上的全局都得到了证明。
Abstract.The time-dependent Navier–Stokes system is studied in a two-dimensional domain with strip-like outlets to infinity in weighted Sobolev function spaces. It is proved that under natural compatibility conditions there exists a unique solution with prescribed fluxes over cross-sections of outlets to infinity which tends in each outlet to the corresponding time-dependent Poiseuille flow. The obtained results are proved for arbitrary large norms of the data (in particular, for arbitrary fluxes) and globally in time.