可压缩Navier-Stokes方程的能控性

项目名称： 可压缩Navier-Stokes方程的能控性

项目编号： No.11501378

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 数理科学和化学

项目作者： 陶强

作者单位： 深圳大学

项目金额： 18万元

中文摘要： 本项目拟研究可压缩Navier-Stokes方程的能控性。所研究的内容来源于航空航天、环境工程和生物医药等领域人们关注的热点问题，如线性化可压缩Navier-Stokes方程和与其密切相关的具记忆项的抛物方程的能控性，高维、完全或粘性依赖密度的可压缩Navier-Stokes方程的能控性。. 我们将着重探讨可压缩Navier-Stokes方程特有结构，如非线性、双曲抛物耦合及粘性等对能控性产生的影响。这些结构中所包含的多重非线性、粘性依赖密度以及退化等性质使得模型能够更加真实反映物理实际，但同时为能控性的研究带来本质困难。因此，我们既需要综合运用分布参数系统控制理论和流体力学方程相关知识，也需要探索新的研究思路与手段。本项目的研究方法和结果将为相关的工程技术问题提供理论依据与指导，并在一定程度上丰富和完善分布参数系统控制理论。

中文关键词： 可压缩Navier-Stokes方程；能控性；线性化Navier-Stokes方程；粘性依赖密度；记忆项

英文摘要： In this project, we study the controllability of the compressible Navier-Stokes equations. The problems arise in aerospace, environmental engineering and biological medicine, etc, including controllability of the linearized compressible Navier-Stokes equations and the parabolic equations with memory and controllability of the multi-dimensional compressible Navier-Stokes equations, the full compressible Navier-Stokes equations or the compressible Navier-Stokes equations with density-dependent viscosity, which are all hot issues.. We focus on studying the influence of the special structures of the Navier-Stokes equations, including nonlinearity, coupling of hyperbolic-parabolic and viscosity, to the controllability. These structures contain multiple nonlinear, density-dependent viscosity and degenerative feature makes the model more real reflect the physical reality, but bring difficulties to our research. So we need both the integrated use of distributed parameter system control theory and fluid mechanics equation related knowledge, also need to explore new research ideas and methods. To a certain extent, our results and methods will provide theoretical basis and guidance for related engineering problems and enrich the theory of distributed parameter system control theory.

英文关键词： compressible Navier-Stokes equation;controllability;linearized Navier-Stokes equation;density-dependent viscosity;memory