Year: 2019
Type: preprint
Abstract: We show the existence of Hölder continuous periodic weak solutions of the 2d Boussinesq equation with diffusive temperature which satisfy the prescribed kinetic energy. More precisely, for any smooth $e(t):[0,1]\rightarrow R_+$ and $\varepsilon\in (0, \frac{1}{10})$, there exist $v\in C^{\frac{1}{10}-\varepsilon}([0,1]\times {\rm T}^2), θ\in C_t^{1,\frac{1}{20}-\frac{\varepsilon}{2}}C_x^{2,\frac{1}{10}-\varepsilon}([0,1]\times {\rm T}^2)$ which solve boussinesq equation in the sense of distribution and satisfy e(t)=\int_{{\rm T}^2}|v(t,x)|^2dx, \quad \forall t\in [0,1].
Source: arXiv (Cornell University)
Authors: Luo, Tianwen, Tao, Tao, Zhang, Liqun
Institution: Tsinghua University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1994844598, 关于流体力学边界层中的一些问题, G624049411
OpenAlex ID: W2914967668