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 - <div style="text-align: justify;">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.&nbsp; 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 $\sigma&gt;0$, we obtain the global well-posedness.&nbsp; A special consequence is the global well-posedness of 2D Boussinesq-Navier-Stokes equations when the dissipation is logarithmically supercritical.</div>