The 2D Boussinesq-Navier-Stokes Equations with Logarithmically Supercritical Dissipation
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@Article{JMS-57-101,
author = {K.C. , Durga JangRegmi , DipendraTao , Lizheng and Wu , Jiahong},
title = {The 2D Boussinesq-Navier-Stokes Equations with Logarithmically Supercritical Dissipation},
journal = {Journal of Mathematical Study},
year = {2024},
volume = {57},
number = {1},
pages = {101--132},
abstract = {
We study the global well-posedness of the initial-value problem for the 2D Boussinesq-Navier-Stokes equations with dissipation given by an operator $\mathcal{L}$ that can be defined through both an integral kernel and a Fourier multiplier. When the operator $\mathcal{L}$ is represented by $\frac{|\xi|}{a(|\xi|)}$ with $a$ satisfying $ \lim_{|\xi|\to \infty} \frac{a(|\xi|)}{|\xi|^\sigma} = 0$ for any $\sigma>0$, we obtain the global well-posedness. A special consequence is the global well-posedness of 2D Boussinesq-Navier-Stokes equations when the dissipation is logarithmically supercritical.
},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v57n1.24.06},
url = {http://global-sci.org/intro/article_detail/jms/22990.html}
}
TY - JOUR
T1 - The 2D Boussinesq-Navier-Stokes Equations with Logarithmically Supercritical Dissipation
AU - K.C. , Durga Jang
AU - Regmi , Dipendra
AU - Tao , Lizheng
AU - Wu , Jiahong
JO - Journal of Mathematical Study
VL - 1
SP - 101
EP - 132
PY - 2024
DA - 2024/03
SN - 57
DO - http://doi.org/10.4208/jms.v57n1.24.06
UR - https://global-sci.org/intro/article_detail/jms/22990.html
KW - Supercritical Boussinesq-Navier-Stokes equations, global regularity.
AB -
We study the global well-posedness of the initial-value problem for the 2D Boussinesq-Navier-Stokes equations with dissipation given by an operator $\mathcal{L}$ that can be defined through both an integral kernel and a Fourier multiplier. When the operator $\mathcal{L}$ is represented by $\frac{|\xi|}{a(|\xi|)}$ with $a$ satisfying $ \lim_{|\xi|\to \infty} \frac{a(|\xi|)}{|\xi|^\sigma} = 0$ for any $\sigma>0$, we obtain the global well-posedness. A special consequence is the global well-posedness of 2D Boussinesq-Navier-Stokes equations when the dissipation is logarithmically supercritical.
Durga Jang K.C., Dipendra Regmi, Lizheng Tao & Jiahong Wu. (2024). The 2D Boussinesq-Navier-Stokes Equations with Logarithmically Supercritical Dissipation.
Journal of Mathematical Study. 57 (1).
101-132.
doi:10.4208/jms.v57n1.24.06
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