Weak solutions to the time-fractional g-Bénard equations

Abstract

In this paper, we introduce the g-Bénard equations with time-fractional derivative of order $\alpha \in (0,1)$ in domains of ${\mathbb{R}}^2$. This equations model, the memory-dependent heat conduction of liquids in fractal media considered in g-framework. We aim to study the existence and uniqueness of weak solutions by means of standard techniques from Navier-Stokes equations theory and fractional calculus theory.

16 pages. arXiv admin note: text overlap with arXiv:2006.02865