# American Institute of Mathematical Sciences

June  2020, 40(6): 3737-3765. doi: 10.3934/dcds.2019230

## Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature

 1 Yau Mathematical Science center, Tsinghua University, Beijing 100084, China 2 School of Mathematics Sciences, Shandong University, Jinan 250100, China 3 Academy of Mathematic and System Science, CAS; School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China

* Corresponding author: Liqun Zhang

Received  December 2018 Revised  March 2019 Published  June 2019

Fund Project: The first author is supported in part by NSFC Grants 11601258.6. The second author is supported by the fundamental research funds of Shandong university under Grant 11140078614006. The third author is partially supported by the Chinese NSF under Grant 11471320 and 11631008

We show the existence of finite kinetic energy solution with prescribed kinetic energy to the 2d Boussinesq equations with diffusive temperature on torus.

Citation: Tianwen Luo, Tao Tao, Liqun Zhang. Finite energy weak solutions of 2d Boussinesq equations with diffusive temperature. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3737-3765. doi: 10.3934/dcds.2019230
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