ON LOCAL CONTROLLABILITY FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY DEPENDENT VISCOSITIES*

doi:10.1007/s10473-023-0213-5

Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (2): 675-685.doi: 10.1007/s10473-023-0213-5

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ON LOCAL CONTROLLABILITY FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY DEPENDENT VISCOSITIES^*

Xiangkai Lian¹, Qiang Tao^2,3,†, Zheng-an Yao⁴

1. College of Mathematics, Sun Yat-sen University, Guangzhou 510275, China;
2. College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China;
3. Shenzhen Key Laboratory of Advanced Machine Learning and Applications, Shenzhen University, Shenzhen 518060, China;
4. College of Mathematics, Sun Yat-sen University, Guangzhou 510275, China

Received:2021-12-07 Revised:2022-02-18 Online:2023-03-25 Published:2023-04-12
Contact: †Qiang Tao, E-mail: taoq060@126.com.
About author:Xiangkai Lian, E-mail: lianxk@mail2.sysu.edu.cn; Zheng-an Yao, E-mail: mcsyao@mail.sysu.edu.cn
Supported by:
This work was partially supported by the National Science Foundation of China (11971320, 11971496), the National Key R $\&$ D Program of China (2020YFA0712500) and the Guangdong Basic and Applied Basic Research Foundation (2020A1515010530).

Abstract

Xiangkai Lian, Qiang Tao, Zheng-an Yao. ON LOCAL CONTROLLABILITY FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY DEPENDENT VISCOSITIES^*[J].Acta mathematica scientia,Series B, 2023, 43(2): 675-685.

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References

[1] Amosova E V.Exact local controllability for equations of the dynamics of a viscous gas (Russian). Differ Uravn, 2011, 47: 1754-1772
[2] Badra M, Ervedoza S, Guerrero S.Local controllability to trajectories for non- homogeneous incompressible Navier-Stokes equations. Ann Inst H Poincaré Non Linear Anal, 2016, 33: 529-574
[3] Chaves-Silva F W, Rosier L, Zuazua E. Null controllability of a system of viscoelasticity with a moving control. J Math Pures Appl, 2014, 101: 198-222
[4] Chowdhury S, Mitra D.Null controllability of the linearized compressible Navier-Stokes equations using moment method. J Evol Equ, 2015, 15: 331-360
[5] Chowdhury S, Mitra D, Ramaswamy M, Renardy M.Null controllability of the linearized compressible Navier-Stokes system in one dimension. J Differential Equations, 2014, 257: 3813-3849
[6] Chowdhury S, Ramaswamy M, Raymond J P.Controllability and stabilizability of the linearized compress- ible Navier-Stokes system in one dimension. SIAM J Control Optim, 2012, 50: 2959-2987
[7] Ervedoza S, Glass O, Guerrero S.Local exact controllability for the two- and three-dimensional compressible Navier-Stokes equations. Comm Partial Differential Equations, 2016, 41: 1660-1691
[8] Ervedoza S, Glass O, Guerrero S, Puel J P.Local exact controllability for the one-dimensional compressible Navier-Stokes equation. Arch Rational Mech Anal, 2012, 206: 189-238
[9] Ervedoza S, Savel M.Local boundary controllability to trajectories for the 1D compressible Navier Stokes equations. ESAIM Control Optim Calc Var, 2018, 24: 211-235
[10] Glass O.Exact boundary controllability of 3-D Euler equation. ESAIM Control Optim Calc Var, 2000, 5: 1-44
[11] Glass O.On the controllability of the 1-D isentropic Euler equation. J Eur Math Soc, 2007, 9: 427-486
[12] Glass O.On the controllability of the non-isentropic 1-D Euler equation. J Differential Equations, 2014, 257: 638-719
[13] Li T T, Rao B P.Exact boundary controllability for quasi-linear hyperbolic systems. SIAM J Control Optim, 2003, 41: 1748-1755
[14] Maity D.Some controllability results for linearized compressible Navier-Stokes system. ESAIM Control Optim Calc Var, 2015, 21: 1002-1028
[15] Martin P, Rosier L, Rouchon P.Null controllability of the structurally damped wave equation with moving control. SIAM J Control Optim, 2013, 51: 660-684
[16] Mitra S.Observability and unique continuation of the adjoint of a linearized simplified compressible fluid- structure model in a 2D channel. ESAIM Control Optim Calc Var, 2021, 27: S18
[17] Molina N.Local exact boundary controllability for the compressible Navier-Stokes equations. SIAM J Control Optim, 2019, 57: 2152-2184
[18] Nersisyan H.Controllability of the 3D compressible Euler system. Comm Partial Differential Equations, 2011, 36: 1544-1564
[19] Simon J.Compact sets in the space $L^{p}$(0, T;B). Ann Mat Pura Appl, 1987, 146: 65-96
[20] Tao Q.Local exact controllability for the planar compressible magnetohydrodynamic equations. SIAM J Control Optim, 2018, 56: 4461-4487
[21] Tao Q.Local exact controllability for a viscous compressible two-phase model. J Differential Equations, 2021, 281: 58-84
[22] Vaigant V A, Kazhikhov A V.On the existence of global solutions of two-dimensional Navier-Stokes equa- tions of a compressible viscous fluid
(in Russian). Sibirsk Mat Zh, 1995, 36: 1283-1316; Translation in Sib Math J, 1995, 36: 1108-1141

ON LOCAL CONTROLLABILITY FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY DEPENDENT VISCOSITIES^*

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