Dynamics of Gaseous Stars and Hydrodynamic Limits for Boltzmann Equations

气态恒星的动力学和玻尔兹曼方程的流体动力学极限

• 批准号: 0908007
• 负责人: Nader Masmoudi
• 金额: $ 9.76万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-07-01 至 2013-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0908007&HistoricalAwards=false
• 关键词: Dynamics; Gaseous; Stars; Hydrodynamic; Limits

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).The first goal of this project is to better understand physical vacuum as a free boundary for solutions to compressible Euler and Navier-Stokes equations with or without forcing and to develop a satisfactory nonlinear stability theory. The physical vacuum naturally appears in astrophysics and gas dynamics: a mathematical study of its behavior will help understand dynamics of gaseous stars. Furthermore, this investigation will lead to a general theory of degenerate hyperbolic equations. The second goal is to derive, with rigorous justification, various fluid equations from Boltzmann equations. Study of hydrodynamic limits for Boltzmann equations is important in connecting the two different subjects of kinetic theory and fluid dynamics. A rigorous study will help understand how large-scale behaviors emerge from dynamics or structures on small scales. In particular, for the Vlasov-Maxwell-Boltzmann system, it will open a new line of research. The compressible Euler and Navier-Stokes fluid equations and the Boltzmann kinetic equations are the basic, challenging models in gas dynamics; they have broad applications in many other areas of science and engineering as well. For example, Euler and Navier-Stokes equations are useful to study shallow water waves, and Boltzmann equations are important for semiconductor theory. The mathematical problems addressed in this project are not only important for the study of these equations, but also of interest in physics and other sciences. A better understanding of them would prompt the study of models for more complex, realistic flows.

该项目的第一个目标是更好地理解作为自由边界的物理真空，以解决可压缩欧拉方程和Navier-Stokes方程（有或没有强迫），并发展一个令人满意的非线性稳定性理论。 物理真空自然地出现在天体物理学和气体动力学中：对其行为的数学研究将有助于理解气态恒星的动力学。 此外，这项研究将导致退化双曲型方程的一般理论。 第二个目标是推导，严格的理由，各种流体方程玻尔兹曼方程。 玻尔兹曼方程的流体力学极限研究是联系运动论和流体力学这两门不同学科的重要环节。 严格的研究将有助于理解大规模的行为是如何从小规模的动力学或结构中产生的。 特别是对于Vlasov-Maxwell-Boltzmann系统，它将开辟一条新的研究路线。可压缩的欧拉和Navier-Stokes流体方程和玻尔兹曼动力学方程是气体动力学中基本的、具有挑战性的模型;它们在许多其他科学和工程领域也有广泛的应用。 例如，欧拉和纳维-斯托克斯方程对研究浅水波很有用，玻尔兹曼方程对半导体理论很重要。 在这个项目中解决的数学问题不仅对这些方程的研究很重要，而且在物理学和其他科学中也很重要。 更好地了解它们将促进对更复杂、更现实的流动模型的研究。