Holder continuous weak solutions of the 2D Boussinesq equation with thermal diffusion  

作　　者：Tianwen Luo Tao Tao Liqun Zhang 

机构地区：[1]Yau Mathematical Sciences Center,Tsinghua University,Beijing 100084,China [2]School of Mathematics,Shandong University,Jinan 250100,China [3]Institute of Mathematics,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [4]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Science China Mathematics》2024年第8期1777-1806,共30页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11971464);supported by National Natural Science Foundation of China(Grant No.11901349);supported by National Natural Science Foundation of China(Grant Nos.11471320 and 11631008)。

摘　　要：We show the existence of Holder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic energy.More precisely,for any smooth e(t):[0,1]→R+andε∈(0,110),there exist v∈C 110−ε([0,1]×T2)andθ∈C 1,120−εt 2 C 2,1 x 10−ε([0,1]×T2),which satisfy(1.1)in the sense of distribution and e(t)=ˆT2|v(t,x)|2 dx,∀t∈[0,1].

关 键 词：2D Boussinesq equation with thermal diffusion Holder continuous periodic weak solutions prescribed kinetic energy 

分 类 号：O175[理学—数学]