Local Exact Controllability for the One-Dimensional Compressible Navier-Stokes Equation

被引：43

作者：

Ervedoza, Sylvain ^{[1
,2
]}

Glass, Olivier ^{[3
]}

Guerrero, Sergio ^{[4
]}

Puel, Jean-Pierre ^{[5
,6
]}

机构：

[1] CNRS, UMR 5219, Inst Math Toulouse, F-31062 Toulouse, France

[2] Univ Toulouse, UPS, INSA, INP,ISAE,UTM,IMT,UT1, F-31062 Toulouse, France

[3] Univ Paris 09, CNRS, Ceremade UMR 7534, F-75775 Paris 16, France

[4] Univ Paris 06, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France

[5] Ikerbasque & BCAM, Derio 48160, Vizcaya, Spain

[6] Univ Versailles, LMV, F-78000 Versailles, France

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2012年 / 206卷 / 01期

关键词：

EXACT BOUNDARY CONTROLLABILITY; GLOBAL-CONTROLLABILITY;

D O I：

10.1007/s00205-012-0534-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we deal with the isentropic (compressible) Navier-Stokes equation in one space dimension and we adress the problem of the boundary controllability for this system. We prove that we can drive initial conditions which are sufficiently close to some constant states to those constant states. This is done under some natural hypotheses on the time of control and on the regularity on the initial conditions.

引用

页码：189 / 238

页数：50

共 20 条

[1]

Albano P., 2000, ELECTRON J DIFFER EQ, P1

[2]

AMOSOVA E.V., 2011, DIFFERENTSI IN PRESS

[3]

[Anonymous], 1996, LECT NOTES SERIES

[4]

[Anonymous], 2007, Mathematical Surveys and Monographs

[5]

[Anonymous], 1996, ESAIM CONTR OPTIM CA, DOI DOI 10.1051/COCV:1996102

[6]

Coron JM, 1996, RUSS J MATH PHYS, V4, P429

[7] Global existence in critical spaces for compressible Navier-Stokes equations [J].

Danchin, R .

INVENTIONES MATHEMATICAE, 2000, 141 (03) :579-614

[8] Local exact controllability of the Navier-Stokes system [J].

Fernández-Cara, E ;

Guerrero, S ;

Imanuvilov, OY ;

Puel, JP .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2004, 83 (12) :1501-1542

[9] Exact boundary controllability of 3-D Euler equation [J].

Glass, O .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2000, 5 :1-44

[10]

Glass O, 2007, J EUR MATH SOC, V9, P427

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