Inhomogeneous Boundary Value Problems for the Three-Dimensional Evolutionary Navier—Stokes Equations
Inhomogeneous Boundary Value Problems for the Three-Dimensional Evolutionary Navier—Stokes Equations
复制标题
三维演化Navier-Stokes方程的非齐次边值问题
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
L. Hou
中科院分区：
文献类型：
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作者：
A. Fursikov;M. Gunzburger;L. Hou
抽象。本文研究了三维Oseen方程和Navier-Stokes方程的非齐次边值问题的可解性：给定Dirichlet边界条件、初始值和右侧强迫函数的函数空间，找到解的函数空间，使得由Oseen方程的边值问题生成的算子在解的空间之间建立同构以及数据空间。存在性和唯一性结果的时间相关的，三维Navier-Stokes方程的解决方案也成立。这些调查的基础上的理论扩展的时间依赖性，螺线管矢量场，这是本文开发的。本文的结果对研究三维Navier-Stokes方程的边界控制最优控制问题是必不可少的。
Abstract. In this paper, we study the solvability of inhomogeneous boundary value problems for the three-dimensional Oseen and Navier—Stokes equations in the following formulation: given function spaces for Dirichlet boundary conditions, initial values, and right-hand side forcing functions, find function spaces for solutions such that the operator generated by the boundary value problem for the Oseen equations establishes an isomorphism between the space of solutions and the spaces of data. Existence and uniqueness results for the solution of the time-dependent, three-dimensional Navier—Stokes equations are also established. These investigations are based on a theory of extensions of time-dependent, solenoidal vector fields that is developed in this paper. The results of this paper are indispensable to the study of optimal control problems with boundary control for the three-dimensional Navier—Stokes equations.