流体动力学方程的数学理论系列讲座(5.20-6.4)

主讲人:吴家宏 教授 (Oklahoma State University, USA )

联系人:许孝精 副教授(北京师范大学, JLIB_HTML_CLOAKING )

简介:美国Oklahoma大学数学系吴家宏(Jiahong Wu)教授将在519日至65日访问我校数学科学学院。此次访问期间吴家宏教授将开设关于不可压缩流体动力学方程的数学理论系列讲座。欢迎有兴趣的研究生、博士生,以及高年级本科生和青年教师参加!

地点:后主楼1124

时间:上午9:15-11:40520, 21, 23, 24, 27, 28, 30, 31,  63, 4

          (即52064日中除去周三,六、日)

Outline of the course

   Aiming at graduate students and young researchers, this course presents the most recent developments on various topics in mathematical fluid mechanics. Particular topics to be covered by this course include: the incompressible Bou- ssinesq equations, the surface quasi-geostrophic (SQG) equation and the incompressible magneto-hydrodynamics (MHD) equations. This course will be self-contained and necessary background information will be provided. Here is a draft syllabus for this course: 

Class 1: Geophysical backgrounds and derivation for the Boussinesq equations

and the SQG equation. Current results on the inviscid 2D Boussinesq 

equations and the fully dissipative Boussinesq equations.

Class 2: The Boussinesq equations with horizontal dissipation or horizontal         

 thermal diffusion.

Class 3: The Boussinesq equations with vertical dissipation and vertical thermal

 diffusion.

Class 4: The Boussinesq equations with fractional dissipation.

Class 5: Review of current results on the critical SQG equation and the super-

 critical SQG equation.

Class 6: Results on the generalized SQG equation.

Class 7: Results on the logarithmically supercritical SQG equation.

Class 8: Review of recent results on the incompressible MHD equations.

Class 9: The MHD equations with mixed partial dissipation.

Class 10: The MHD equations with horizontal dissipation and horizontal magne-

 tic diffusion. 

  The references for this course include a long list of recent publications(not listed here but will be provided during the lectures) and some preparation books listed below:

[1] H. Bahouri, J.-Y. Chemin and R. Danchin, Fourier Analysis and Nonlinear

 Partial Differential Equations, Springer, 2011.

[2] A.J. Majda and A.L. Bertozzi, Vorticity and Incompressible Flow, Cambri- 

 dge University Press, 2001.

[3] C. Miao, J. Wu and Z. Zhang, Littlewood-Paley Theory and its Applications

 in Partial Differential Equations of Fluid Dynamics, Science Press, Beijing,

 China, 2012.

额外信息