HÖLDER CONTINUOUS SOLUTIONS OF BOUSSINESQ EQUATIONS

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (5): 1591-1616.

HÖLDER CONTINUOUS SOLUTIONS OF BOUSSINESQ EQUATIONS

Tao TAO¹, Liqun ZHANG²

1. School of Mathematics Sciences, Peking University, Beijing 100871, China;School of Mathematics, Shandong University, Jinan 250100, China;
2. Academy of Mathematic and System Science, CAS, Beijing 100190, China;School of Mathematical Sciences, UCAS, Beijing 100049, China

收稿日期:2017-04-01 出版日期:2018-11-09 发布日期:2018-11-09
作者简介:Tao TAO,E-mail:taotao@amss.ac.cn;Liqun ZHANG,E-mail:lqzhang@math.ac.cn
基金资助:
The research was partially supported by the NSFC (11471320 and 11631008).

HÖLDER CONTINUOUS SOLUTIONS OF BOUSSINESQ EQUATIONS

Tao TAO¹, Liqun ZHANG²

1. School of Mathematics Sciences, Peking University, Beijing 100871, China;School of Mathematics, Shandong University, Jinan 250100, China;
2. Academy of Mathematic and System Science, CAS, Beijing 100190, China;School of Mathematical Sciences, UCAS, Beijing 100049, China

Received:2017-04-01 Online:2018-11-09 Published:2018-11-09
Supported by:
The research was partially supported by the NSFC (11471320 and 11631008).

摘要/Abstract

摘要： We show the existence of dissipative Hölder continuous solutions of the Boussinesq equations. More precise, for any β ∈ (0, 1/5), a time interval[0, T] and any given smooth energy profile e:[0, T] → (0, ∞), there exist a weak solution (v, θ) of the 3d Boussinesq equations such that (v, θ) ∈ C^β(T³×[0, T]) with e(t)=∫_T³|v(x, t)|²dx for all t ∈[0, T]. This extend the result of [2] about Onsager's conjecture into Boussinesq equation and improve our previous result in [30].

关键词: Boussinesq equations, Hölder continuous solutions, prescribed kinetic energy

Abstract: We show the existence of dissipative Hölder continuous solutions of the Boussinesq equations. More precise, for any β ∈ (0, 1/5), a time interval[0, T] and any given smooth energy profile e:[0, T] → (0, ∞), there exist a weak solution (v, θ) of the 3d Boussinesq equations such that (v, θ) ∈ C^β(T³×[0, T]) with e(t)=∫_T³|v(x, t)|²dx for all t ∈[0, T]. This extend the result of [2] about Onsager's conjecture into Boussinesq equation and improve our previous result in [30].

Key words: Boussinesq equations, Hölder continuous solutions, prescribed kinetic energy

Tao TAO, Liqun ZHANG. HÖLDER CONTINUOUS SOLUTIONS OF BOUSSINESQ EQUATIONS[J]. 数学物理学报(英文版), 2018, 38(5): 1591-1616.

Tao TAO, Liqun ZHANG. HÖLDER CONTINUOUS SOLUTIONS OF BOUSSINESQ EQUATIONS[J]. Acta Mathematica Scientia, 2018, 38(5): 1591-1616.

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HÖLDER CONTINUOUS SOLUTIONS OF BOUSSINESQ EQUATIONS

HÖLDER CONTINUOUS SOLUTIONS OF BOUSSINESQ EQUATIONS

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