Optimal Boundary Control for the Evolutionary Navier--Stokes System: The Three-Dimensional Case
Optimal Boundary Control for the Evolutionary Navier--Stokes System: The Three-Dimensional Case
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DOI：
10.1137/s0363012904400805
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发表时间：
2005-06
期刊：
影响因子：
--
通讯作者：
A. Fursikov;M. Gunzburger;L. Hou
中科院分区：
文献类型：
--
作者：
A. Fursikov;M. Gunzburger;L. Hou
研究了三维有界区域外发展的Navier-Stokes方程的最优边界控制问题。控制通过Dirichlet边界条件实现，并在速度场迹空间的一个子集中以几乎最小的可能正则性进行搜索。控制目标是使阻力泛函最小。证明了最优解的存在性。基于本文建立的具有规则初值但不满足相容条件的伴随Osee方程的正则性结果，导出了最优性方程组的一种强形式。
Optimal boundary control problems for the three-dimensional, evolutionary Navier--Stokes equations in the exterior of a bounded domain are studied. Control is effected through the Dirichlet boundary condition and is sought in a subset of the trace space of velocity fields with almost minimal possible regularity. The control objective is to minimize the drag functional. The existence of an optimal solution is proved. A strong form of an optimality system of equations is derived on the basis of regularity results established in this work for the adjoint Oseen equations with regular initial data which do not satisfy the compatibility conditions.