On the dynamic programming approach for the 3D Navier-Stokes equations

被引：2

作者：

Manca, Luigi ^{[1
]}

机构：

[1] Univ Padua, Dipartimento Matemat Pura & Applicata, I-35121 Padua, Italy

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2008年 / 57卷 / 03期

关键词：

Navier-Stokes equations; dynamic programming; Hamilton-Jacobi-Bellman equations;

D O I：

10.1007/s00245-007-9024-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated Hamilton-Jacobi-Bellman equation is proved. Finally, existence of an optimal control through the feedback formula and of an optimal state is discussed.

引用

页码：329 / 348

页数：20

共 50 条

[1] On the Dynamic Programming Approach for the 3D Navier–Stokes Equations
Luigi Manca
Applied Mathematics and Optimization, 2008, 57 : 329 - 348
[2] The 3D Navier-Stokes equations seen as a perturbation of the 2D Navier-Stokes equations
Iftimie, D
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 324 (03): : 271 - 274
[3] The 3D Navier-Stokes equations seen as a perturbation of the 2D Navier-Stokes equations
Iftimie, D
BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1999, 127 (04): : 473 - 517
[4] Dynamic programming for the stochastic Navier-Stokes equations
da Prato, G
Debussche, A
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2000, 34 (02): : 459 - 475
[5] DYNAMIC-PROGRAMMING OF THE NAVIER-STOKES EQUATIONS
SRITHARAN, SS
SYSTEMS & CONTROL LETTERS, 1991, 16 (04) : 299 - 307
[6] 3D STEADY COMPRESSIBLE NAVIER-STOKES EQUATIONS
Pokorny, Milan
Mucha, Piotr B.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2008, 1 (01): : 151 - 163
[7] REGULARITY CONDITIONS FOR THE 3D NAVIER-STOKES EQUATIONS
Fan, Jishan
Gao, Hongjun
QUARTERLY OF APPLIED MATHEMATICS, 2009, 67 (01) : 195 - 199
[8] Partial Regularity for the 3D Navier-Stokes Equations
Robinson, James C.
MATHEMATICAL ANALYSIS OF THE NAVIER-STOKES EQUATIONS, 2020, 2254 : 147 - 192
[9] Asymptotic stability for the 3D Navier-Stokes equations
Zhou, Y
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2005, 30 (1-3) : 323 - 333
[10] On the energy equality for the 3D Navier-Stokes equations
Berselli, Luigi C.
Chiodaroli, Elisabetta
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2020, 192

← 1 2 3 4 5 →