We shall explain the main idea of the construction of weak solutions of Euler equations.  Such construction goes back J. Nash's work, on the proof C^1 isometric embedding.
Then we consider the application of the convex integration mothed to the Boussingesq equations.
The Boussingesq equations was introduced in understanding the coupling nature of the thermodynamics and the fluid dynamics.
We prove the existence of continuous periodic weak solutions of the Boussinesq equations which either satisfies the prescribed kinetic energy or some other property. 
This is a jointed work with Tao tao.

个人简介🙂‍↕️：张立群，1989年于中科院系统所获得博士学位，2003年获国家基金委杰出青年基金🤴🏿，国务院政府特殊津贴。现为中国科杏悦数学与系统科学研究院研究员🧑‍🎨。

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