LOCAL EXACT CONTROLLABILITY TO THE TRAJECTORIES OF THE NAVIER-STOKES SYSTEM WITH NONLINEAR NAVIER-SLIP BOUNDARY CONDITIONS

Sergio Guerrero

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LOCAL EXACT CONTROLLABILITY TO THE TRAJECTORIES OF THE NAVIER-STOKES SYSTEM WITH NONLINEAR NAVIER-SLIP BOUNDARY CONDITIONS

机译：具有非线性滑移边界条件的NAVIER-STOKES系统轨迹的局部精确可控性

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In this paper we deal with the local exact controllability of the Navier-Stokes system with nonlinear Navier-slip boundary conditions and distributed controls supported in small sets. In a first step, we prove a Carleman inequality for the linearized Navier-Stokes system, which leads to null controllability of this system at any time T > 0. Then, fixed point arguments lead to the deduction of a local result concerning the exact controllability to the trajectories of the Navier-Stokes system.

机译：在本文中，我们处理带有非线性Navier滑移边界条件和小集支持的分布式控制的Navier-Stokes系统的局部精确可控制性。第一步，我们证明了线性化Navier-Stokes系统的Carleman不等式，它在T> 0的任何时间导致该系统的零可控性。然后，不动点参数导致推导与精确可控性有关的局部结果Navier-Stokes系统的轨迹。

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来源
《ESAIM》 |2006年第2006期|p.484-544|共61页
作者
Sergio Guerrero;
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作者单位

Dpto. E.D.A.N., University of Sevilla, Aptdo. 1160, 41080 Sevilla, Spain;

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原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
navier-stokes system; controllability; slip;

机译：航海系统;可控制性;滑移;

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1. Local null controllability of the N-dimensional Navier-Stokes system with nonlinear Navier-slip boundary conditions and N-1 scalar controls [J] . Guerrero Sergio, Montoya Cristhian Journal de Mathematiques Pures et Appliquees . 2018,第期

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2. LOCAL EXACT CONTROLLABILITY OF THE NAVIER-STOKES EQUATIONS WITH THE CONDITION ON THE PRESSURE ON PARTS OF THE BOUNDARY [J] . Kim T, Cao DM SIAM Journal on Control and Optimization . 2010,第6期

机译：Navokes-Stokes方程在局部压力作用下的局部精确可控制性
3. Local exact controllability to the trajectories of the Korteweg-de Vries-Burgers equation on a bounded domain with mixed boundary conditions [J] . Cerpa Eduardo, Montoya Cristhian, Zhang Bingyu Journal of Differential Equations . 2020,第9期

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4. EXACT LINEARIZATION OF NONLINEAR SYSTEMS: TRAJECTORY TRACKING WITH BOUNDED CONTROLS AND STATE CONSTRAINTS [C] . J.L. Mancilla Aguilar, R.A. Garcia, C.E. DAttellis Midwest symposium on circuits and systems;MWSCAS . 1996

机译：非线性系统的精确线性化：具有约束控制和状态约束的弹道跟踪
5. CONTROL OF DISTRIBUTED PARAMETER SYSTEMS WITH NONLINEAR BOUNDARY CONDITIONS [D] . UZGIRIS, SARUNAS C. 1966

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6. Local E-optimality Conditions for Trajectory Design to Estimate Parameters in Nonlinear Systems [O] . Andrew D. Wilson, Todd D. Murphey -1

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7. Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions [O] . Guerrero Sergio 2006

机译：具有非线性Navier滑移边界条件的Navier-Stokes系统轨迹的局部精确可控制性

LOCAL EXACT CONTROLLABILITY TO THE TRAJECTORIES OF THE NAVIER-STOKES SYSTEM WITH NONLINEAR NAVIER-SLIP BOUNDARY CONDITIONS

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