An Optimal Control Problem for the Navier-Stokes Equations with Point Sources

被引：3

作者：

Fuica, Francisco ^{[1
]}

Lepe, Felipe ^{[2
]}

Otarola, Enrique ^{[1
]}

Quero, Daniel ^{[1
]}

机构：

[1] Univ Tecn Federico Santa Maria, Valparaiso, Chile

[2] Univ Bio Bio, Concepcion, Chile

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2023年 / 196卷 / 02期

关键词：

Optimal control problems; Navier-Stokes equations; Dirac measures; Muckenhoupt weights; First- and second-order optimality conditions; WEIGHTED NORM INEQUALITIES; ELLIPTIC CONTROL-PROBLEMS; ERROR ANALYSIS; APPROXIMATION; REGULARITY; SPACES; COST;

D O I：

10.1007/s10957-022-02148-2

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

We analyze, in two dimensions, an optimal control problem for the Navier-Stokes equations where the control variable corresponds to the amplitude of forces modeled as point sources; control constraints are also considered. This particular setting leads to solutions to the state equation exhibiting reduced regularity properties. We operate under the framework of Muckenhoupt weights, Muckenhoupt-weighted Sobolev spaces, and the corresponding weighted norm inequalities and derive the existence of optimal solutions and first- and, necessary and sufficient, second-order optimality conditions.

引用

页码：590 / 616

页数：27

共 33 条

[1] Powers of Distances to Lower Dimensional Sets as Muckenhoupt Weights [J].